in 

CO 
ri- 

Cvi 
O 


IV. 


LIBRARY 


UNIVERSITY  OF  CALIFORI 


OF" 


Received 
Accession  No. 


,  189 


.    Claxs  No. 


n  . 


Neiv  lievised  Edition. 


JUVENILE 


MENTAL  ARITHMETIC; 


AN  INTRODUCTION  TO  THE 


'AMERICAN  INTELLECTUAL  ARITHMETIC." 


BY  JOHN  P.  STODDARD,  A.M., 

AUTHOR   OP  TILE  "NOSMAL  MATHEMATICAL  SBK1ES,"   JC1C. 


NEW  YOKK: 
SHELDON     &     COMPANY. 

CLEVELAND:  INGUAM  A  BEAGQ.     CINCINNATI:  APPLEOATB  A  o<x 
DKTROIT:  E.  B.  SMITH  &  co.     C-IIICAGO:  w.  B.  KJCKN  A  co. 


THE  NOEMAL  MATHEMATICAL  SEEIES. 

STODDARD'S  JUVENILE  MENTAL  ARITHMETIC.  25  cents. 
STODDARD'S  INTELLECTUAL  ARITHMETIC.  Price  40  cents. 
STODDARD'S  RUDIMENTS  OF  ARITHMETIC.  Price  50  cents. 
STODDAED'S  NEW  PRACTICAL  ARITHMETIC.  Price  $1  00. 
STODDARD  &  HENKLE'S  ELEMENTAEYALGEBRA.  $1  25. 
STODDARD  &  IIENKLE'S  UNIVERSITY  ALGEBRA.  $2-  00. 
METHODS  OF  TEACHING  AND  KEY  TO  STODDARD'S 

INTELLECTUAL    ARITHMETIC.     Price  50  cents. 
KEY  TO  STODDARD'S  PRACTICAL  ARITHMETIC.    Price  $1  00. 
KEY  TO  S.  &  H.'S  ELEMENTARY  ALGEBRA.    Price  $1  25. 
KEY  TO  S.  &  H.'S  UNIVERSITY  ALGEBRA.    Price  $2  00. 


Entered,  according  to  Act  of  Congress  in  the  year  1857,  by 

SHELDON,  BLAKEMAN  &  CO., 

In  the  Clerk's  Office,  of  the  District  Court  of  the  United  States  for 
the  Southern  District  of  New  York. 


Re-entered,  according  to  Act  of  Congress,  in  the  year  1865,  by 

SHELDON   &   COMPANY, 

In  the  Clerk's  Office,  of  the  District  Court  of  the  United  States  for 
the  Southern  District  of  New  York. 


Electrotyped  by  SMITH  &  McDouoAL,  82  &  84  Beekman  St.,  M.  Y. 


PREFACE. 


The  foundation  for  a  thorough  education  is  laid  in 
youth.  The  habits  of  thought,  and  modes  of  reasoning 
then  acquired  will  exert  an  influence  favorable  or  unfa- 
vorable to  intellectual  development  in  after  years.  It  is 
hoped  that  this  little  book,  in  its  scope  and  arrangement, 
and  in  the  discussion  of  the  subjects  of  which  it  treats, 
is  adapted  to  the  capacity  of  young  pupils ;  and  that  by 
proper  instruction  and  careful  study,  it  will  produce  the 
desired  effect  upon  the  mind,  and  afford  the  information 
it  is  designed  to  impart 

Addition,  Subtraction,  Multiplication,  Division,  the 
Tables  of  Weights  and  Measures,  and  the  elementary 
parts  of  Common  Fractions  have  been  introduced  and 
illustrated  by  appropriate  examples. 


SUGGESTIONS  TO  TEACHERS. 

For  the  benefit  of  those  whose  experience  is  limited,  I 
make  the  following  suggestions  in  regard  to  the  most 
approved  methods  of  teaching  this  important  branch  of 
study  : 

The  lesson  should  be  assigned  previous  to  recitation,  to 
afford  the  pupils  an  opportunity  for  its  examination :  the 
use  of  the.  book,  by  the  pupil,  during  class  exercise, 
should  be  prohibited. 

A  question  should  be  read  slowly  and  distinctly,  and 
the  pupil  required  to  repeat  and  analyze  it  without  inter- 
ruption, unless  it  be  to  make  a  necessary  criticism  or  cor- 
rection. 

The  pupils  should  be  called  upon  promiscuously  and 
not  in  rotation,  to  take  part  in  the  recitation. 

Care  should  be  taken  that  the  language  they  use  be 
strictly  correct  as  to  construction  and  articulation. 

If  not  carefully  guarded,  pupils,  in  their  hurried  solu- 
tions, pronounce  many  simple  words  incorrectly.  For 
instance,  the  words :  and,  of,  if,  for,  with,  what,  ichich, 
where,  when,  costs,  quarts,-' etc.,  are  not  unirequently  pro- 
nounced :  an,  off,  ef,  fur,  withe,  wat,  witc?i,  'jcqre,  wen,  coss, 
quats,  etc. 

By  careful  attention  to  these  particulars,  a  lesson  in 
Mental  Arithmetic  is  a  practical  lesson  in  elocution,  gram- 
mar, rhetoric  and  logic,  as  well  as  a  lesson  in  the  science 
of  numbers. 

It  is  respectfully  suggested  that  the  particular  forms 
given  for  the  analysis  of  questions  be  adhered  to,  unless 
letter  ones  should  be  devised  by  the  teacher.  J.  F.  S. 

&&~  Those  wishing  to  become  thoroughly  acquainted  with  Frac- 
tions  and  arithmetical  questions  of  almost  every  kind,  are  referred  to 
Btoddard's  "  American  Intellectual  Arithmetic." 


AEITHMETIC. 


A  Number  expresses  how  many. 
Numbers  are  expressed  in  three  ways  : 

1.  By  words  ;  as,  one,  two,  three,  four,  etc. 

2.  By  figures  ;  as,  1,  2,  3,  4,  5,  6,  7,  8,  9,  and  0. 

3.  By  letters  ;  as,  I,  Y,  X,  L,  C,  D,  and  M. 

The  method  of  expressing  numbers  by  figures 
is  called  the  AKABIC  METHOD. 

The  method  of  expressing  numbers  by  letters 
is  called  the  EOMAN  METHOD. 

Count  the  number  of  stars  in  each  row,  also, 
the  number  in  each  column,  and  express  the 
number  in  each  by  the  different  methods : 


One. 
Two. 

* 

* 
* 

1. 

2. 

Three. 

* 

* 

* 

3. 

Four. 

*      * 

* 

* 

4. 

Five. 

*    *    * 

* 

* 

5. 

Six. 

* 

*    *    * 

* 

* 

6. 

Seven. 

*      * 

*      *      * 

* 

* 

7. 

Eight 

#      *      # 

*    *    * 

* 

* 

8. 

Nine. 

*      *      *      * 

#      *      * 

* 

* 

9. 

Ten.     * 

*      *      *      * 

5k              jli              ifc 

* 

* 

10. 

i, 

2,        3,        4,        5, 

6,        T,        8, 

9, 

10. 

IP 

II,    III,   IV,    V, 

VI,  VII,  VIII, 

IX, 

X. 

MENTAL   ARITHMETIC. 


ARABIC     AND    ROMAN    NUMBERS. 

The  Arabic  and  Roman  methods  of  expressing 
numbers  are  as  follows  : 


ARABIC 
FIGURES. 

If 

NUMBERS. 

ARABIC 
FIGURES. 

&  $ 

il 

NUMBERS. 

0 

Naught. 

20 

XX 

Twenty. 

1 

I 

One. 

21 

XXI 

Twenty-one, 

2 

II 

Two. 

22 

XXII 

Twenty-  two. 

3 

III 

Three. 

23 

XXIII 

Twenty-  three. 

4 

IV 

Pour. 

24 

XXIV 

Twenty-four. 

5 

V 

Five. 

25 

XXV 

Twenty-five. 

6 

VI 

Six. 

26 

XXVI 

Twenty-six. 

7 

YII 

Seven. 

27 

XXVII 

Twenty-seven. 

8 

VIII 

Eight 

28 

XXVIII 

Twenty-eight. 

9 

IX 

Nine. 

29 

XXIX 

Twenty-nine. 

10 

X 

Ten. 

30 

XXX 

Thirty. 

11 

XI 

Eleven. 

40 

XL 

Forty. 

12 

XII 

Twelve. 

50 

L 

Fifty. 

13 

XIII 

Thirteen. 

60 

LX 

Sixty. 

14 

XIV 

Fourteen. 

70 

LXX 

Seventy. 

15 

XV 

Fifteen. 

80 

LXXX 

Eighty. 

16 

XVI 

Sixteen. 

90 

XC 

Ninety. 

17 

XVII 

Seventeen. 

100 

C 

One  Hundred. 

18 

XVIII 

Eighteen. 

500 

D 

Five  Hundred. 

19 

XIX 

Nineteen.  1000 

M 

One  Thousand. 

ADDITION. 


LESSON     I. 

1.  How     many     are     2  and     1  ? 
ANALYSIS. — Two  and  one  are  3. 

2.  How     many     are     2  and     2  ? 

3.  How     many     are     2  and     3  ? 
4r.  How     many     are     2  and     4  ? 

5.  How     many     are     2  and     5  ? 

6.  How     many     are     2  and     6  ? 

7.  How     many     are     2  and     7  ? 

8.  How     many     are     2  and     8  ? 

9.  How     many     are     2  and     9  ? 

10.  How     many     are     2  and  10  ? 

11.  2     and     2     are    .how  many  ? 

12.  2     and     5     are     how  many  ? 

13.  2     and     9     are     how  many  ? 
14:.  2     and     8     are     how  many  ? 

15.  2     and     6     are     how  many  ? 

16.  2     and     4     are     how  many  ? 

17.  2     and     3     are     how  many  ? 

18.  2     and     7     are     how  many  ? 

19.  2     and  10     are    how  many  ? 


LESSON    II. 

1.  Henry  had  4  apples,  and  bought  2  more ; 
how  many  did  he  then  have  ? 

ANALYSIS. — If  Henry  had  4  apples,  and  should  buy 
2  more,  he  would  then  have  4  apples  and  2  apples, 
which  are  6  apples. 


8  ADDITION. 

2.  Harvey  had  5  books,  and  James  had  2 ; 
how  many  books  did  both  have  ? 

3.  Mary  has  3  peaches,  and  John  gave  her  2 
more ;  how  many  peaches  did  she  then  have  ? 

4.  Moses  had  2  cents,  and  his  father  gave  him 
8  more ;  how  many  cents  did  he  then  have  ? 

5.  Edwin  had  10  marbles,   and  found  two 
more  ;  how  many  marbles  did  he  then  have  ? 

G.  Catharine  had  6  pinks,  and  Mary  gave 
her  2  more  ;  how  many  had  Catharine  then  ? 

7.  Alice  found  9  pins,  and  her  mother  gave 
her  2  more  ;  how  many  did  Alice  then  have  ? 

8.  Francis  spelled  7  words  correctly  and  2 
incorrectly ;   how  many  words  were  given  to 
him? 


LESSON    III. 


1. 

How     many 

are     3 

and     1  ? 

2. 

How     many 

are     3 

and     2  ? 

3. 

How     many 

are     3 

and     3  ? 

4. 

How     many 

are     3 

and     4  ? 

5. 

How     many 

are     3 

and     5  ? 

6. 

How     many 

are     3 

and     G  ? 

7. 

How     many 

are     3 

and     7? 

8. 

How     many 

are     3 

and     8  ? 

9. 

How    many 

are     3 

and     9  2 

10. 

How    many 

are    3 

and  10  I 

11. 

4     and     3 

are    how 

many  2 

12. 

3     and     3 

are     how 

many  2 

13. 

2     and     3 

are     how 

many  2 

14. 

G     and     3 

are     how 

many  2 

ADDITION. 


15.  8  and     3  are  how  many  ? 

16.  3  and  10  are  how  many  ? 

17.  3  and     7  are  how  many  ? 

18.  5  and     3  are  how  many  ? 

19.  11  and     3  are  how  many  2 


LESSON    IV, 

1.  If  a  ball  cost  6  cents,  and  a  top  cost  3 
cents,  how  much  will  both  cost  ? 

ANALYSIS. — If  a  ball  cost  6  cents,  and  a  top  cost  3 
cents,  both  will  cost  the  sum  of  6  cents  and  3  cents, 
which  is  9  cents. 

2.  A  boy  paid  3  cents  for  a  cake,  and  2  cents 
for  an  orange ;  how  much  did  he  pay  for  both  ? 

3.  Emily  bought  a  melon  for  10  cents,  and  a 
lemon  for  three  cents ;  what  did  she  give  for 
both? 

4.  There  were  9  boys  on  one  bench,  and  3 
on  another ;  how  many  boys  were  on  both  ? 

5.  Harriet  had  8  sweet  apples  and  3  sour 
ones  ;   how  many  apples  had  she  in  all  ? 

6.  Hezekiah  shot  5  red  squirrels  and  3  gray 
ones ;  how  many  squirrels  did  he  shoot  in  all  ? 

7.  Darius  had  3  books,  and  his  father  gave 
him  3  more  ;  how  many  books  had  he  then  ? 

8.  Fanny  had  6  plums,  and  her  sister  gave 
her  3  more ;  how  many  plums  had  she  then  ? 

9.  Betsy  gave  7  cents  for  tape,  and  3  cents 
for  thread ;  what  did  she  pay  for  both  ? 

10.  Theda  gave  11  cents  "for  a  comb,  and  3 
cents  for  some  hair-pins ;  how  many  cents  did 
she  pay  for  all  ? 


10  ADDITION. 


LESSON    V. 

1.  How     many     are    4     and     1 ! 

2.  How     many     are    4    and    2  ? 

3.  How     many     are    4     and     3  ? 

4.  How     many     are    4     and    4  ? 

5.  How     many     are    4     and     5  ? 

6.  How     many     are     4     and     6  ? 

7.  How     many     are     4     and    7  ? 

8.  How     many     are    4     and     8  ? 

9.  How     many     are    4     and     9  ? 

10.  How     many     are     4     and  10  ? 

11.  4     and     3     are     how     many  ? 

12.  4     and     6     are     how    many  ? 

13.  2     and    4     are     how     many  ? 

14.  4     and     4    are    how    many  ? 

15.  7     and     4     are     how    many  ? 

16.  4     and     8     are     how    many  ? 

17.  5     and     4     are    how    many  ? 

18.  10     and     4     are    how    many  ? 

19.  9     and     4     are     how     many  ? 

20.  4     and  11     are     how    many  ? 


LESSON    VI. 

1.  Sarah  had  4  rings  on  one  finger,  and  3  on 
another ;  how  many  had  she  on  both  fingers  ? 

2.  Walter  has  9  chickens,  and  William  4 ; 
how  many  have  both  ? 

3.  Bought  a  pencil  for  6  cents,  and  a  piece 
of  rubber  for  4  cents ;  what  did  I  pay  for  both  ? 


ADDITION.  11 

4:.  Bought  a  bottle  of  ink  for  10  cents,  and  a 
pen  for  4:  cents ;  what  was  the  cost  of  both  ? 

5.  If  a  lemon  cost  4:  cents,  and  a  peach  cost 
2  cents,  what  was  the  cost  of  both  ? 

6.  Gave  4:  dollars  for  a  hat,  and  4  dollars 
for  a  vest ;  what  was  the  cost  of  both  ? 

7.  Jane  gave  7  cents  for  raisins,  and  4:  cents 
for  cinnamon ;  what  did  she  pay  for  all  ? 

-     8.  If  a  writing-book  cost  5  cents,  and  a  box 
of  pens  cost  4:  cents,  what  did  all  cost? 

9.  After  a  cat  caught  4:  of  Nancy's  chickens, 
she  had  but  11  left;    how  many  had  she  at 
first? 

10.  A  boy,  after  losing  4:  marbles,  had  only 
12  remaining ;  how  many  had  he  at  first  ? 


LESSON    VII. 

1.      How     many     are     5     and     1  ? 


2. 

How 

many 

are 

5 

and 

2? 

3. 

How 

many 

are 

5 

and 

3? 

4. 

How 

many 

are 

5 

and 

*! 

5. 

How 

many 

are 

5 

and 

5? 

6. 

How 

many 

are 

5 

and 

6? 

7. 

How 

many 

are 

5 

and 

7? 

8. 

How 

many 

are 

5 

and 

8? 

9. 

How 

many 

are 

5 

and 

9? 

10. 

How 

many 

are 

5 

and 

10? 

11.  3     and     5     are     how    many  ? 

12.  2     and     5     are    how    many  ? 

13.  6     and     5     are    how    many  ? 


J  2  ADDITION. 

14.  5  and  4  are  how  many  ? 

15.  5  and  5  are  how  many  ? 

16.  7  and  5  are  how  many  ? 

17.  9  and  5  are  how  many  ? 

18.  5  and  8  are  how  many  ? 

19.  10  and  5  are  how  many  ? 

20.  11  and  5  are  how  many  ? 


LESSON    VIII. 

1.  If  Charles  walk  4  miles  in  one  day,  and 
5  miles  in  another,  how  far  does  he  walk  in  the 
two  days  ? 

2.  If  Rebecca  has  5  roses,  and  Mary  gives 
her  3  more,  how  many  will  she  have  then  ? 

3.  If  Joshua  has  5  cakes,  and  Jane  gives 
him  2  more,  how  many  will  he  then  have  ? 

4.  Thomas  gave  8  apples  to  his  companions, 
and  had  5  remaining ;    how  many  had  he  at 
first? 

5.  Gave  5  dollars  for  a  pair  of  pantaloons, 
and  6  dollars  for  a  hat ;  what  did  both  cost  ? 

6.  Andrew  caught  9  birds,  and  Anthony  5 ; 
how  many  did  both  catch  ? 

7.  Baldwin,    after   spending    5    cents,   had 
only  7  cents  remaining  ;  how  many  had  he  at 
first? 

8.  Martha  bought  a  ribbon  for  10  cents,  and 
thread  for   5   cents ;    what  was  the   cost   of 
both? 

9.  Caroline  had  5  flowers,  and  Clarinda  had 
5 ;  how  many  did  both  have  ? 


ADDITION.  13 

10.  Bought  a  bock  for  11  cents,  and  had  5 
cents  remaining ;  how  much  had  I  at  first  ? 

LESSON    IX. 

1.  How     many     are     6  and     1  ? 

2.  How     many     are     G  and     2  ? 

3.  How     many     are     6  and     3  ? 

4.  How     many     are     6  and     4  ? 

5.  How     many     are     6  and     5  ? 

6.  How     many     are     6  and     6  ? 

7.  How""  many     are     7  and     G  ? 

8.  How     many     are     8  and     G  '? 

9.  How    many     are     9  and     6  ? 

10.  How    many     are     G  and  10  ? 

11.  3     and     G     are     how  many  ? 

12.  G     and     4     are     how  many  ? 

13.  G     and     8     are     how  many  ? 

14.  G     and     2     are     how  many  ? 

15.  G     and     5     are     how  many  ? 
1G.  7     and     G     are     how  many  ? 

17.  9     and     G     are     how  many  ? 

18.  10     and     G     are     how  many  ? 

19.  G     and     G     are     how  many  ? 

20.  6     and  11     are     how  many  ? 


LESSON    X. 

1.  Augustus  killed  G  birds,  and  John  2 ;  how 
many  did  both  kill  ? 

2.  Gave  5  cents  to  Franklin,  and  G  cents  to 
Foster  ;  how  many  cents  did  both  receive  2 

2 


14  ADDITION. 

3.  (jrranville  gave  me  1  apples,  and  Mary 
gave  me  6  ;  how  many  did  both  give  me  ? 

4.  A  farmer   having   6   cows,  purchased  3 
more ;  how  many  had  he  then  ? 

5.  Jackson  bought   8  papers,  and  found  6 
more  ;  how  many  had  he  then  ? 

6.  Anna  had  6  pictures,  and  her  brother  gave 
her  6  more ;  how  many  had  she  then  ? 

7.  A  farmer  sold  9  horses,  and  had  6  remain- 
ing ;  how  many  had  he  at  first  ? 

8.  A  market-woman  sold  6  oranges,  and  had 
Y  remaining  ;  how  many  had  she  at  first  ? 

9.  A  boy  sold  10  apples,  and  had"  6  remain- 
ing ;  how  many  had  he  at  first  ? 

10.  After  losing  6  chestnuts  I  had  11  remain- 
ing ;  how  many  had  I  at  first  ? 


LESSON    XI. 

1.  How     many     are     7     and     1  ? 

2.  How     many     are     7     and     2  ? 

3.  How     many     are     7     and     3  ? 

4.  How     many     are     7     and     4  ? 

5.  How     many     are     7     and     5  ? 

6.  How     many     are     7     and     6  ? 
i".  How     many     are     7     and     7  ? 

8.  How     many     are     7     and     8  ? 

9.  How     many     are     7     and     9  ? 

10.  How     many     are     7     and  10  ? 

11.  7     and     4     are     how     many  ? 

12.  2     and     7     are     how     many  ? 

13.  7     and     5     are    how    many  ? 


ADDITION.  15 

14.  3  and    7  are  how  many  ? 

15.  7  and     6  are  how  many  ? 

16.  7  and     9  are  liow  many  ? 

17.  7  and     7  are  how  many  ? 

18.  10  and     7  are  how  many  ? 

19.  8  and     7  are  how  many  ? 

20.  7  and  11  are  how  many  ? 


LESSON    XII. 

1.  A  merchant  bought  4  barrels  of  sugar, 
and  7  barrels  of  molasses  ;  how  many  barrels 
did  he  then  have  ? 

2.  Albert  is  7  years  old,  and  Austin  is  6; 
what  is  the  sum  of  their  ages  ? 

3.  Alfred  solved  8  questions  in  arithmetic, 
and  Abraham  7 ;  how  many  did  both  solve  ? 

4.  If  it  take  7  yards  of  calico  for  a  dress,  and 
2  yards  of  cloth  for  a  cloak,  how  many  will  it 
take  for  both  ? 

5.  Isaac  bought  7  sheets  of  paper,  and  3  more 
Were  given  to  him ;  how  many  had  he  then  ? 

6.  If  a  peck  of  apples  cost  7  cents,  and  a 
peck  of  pears  10  cents,  what  did  both  cost  ? 

7.  Jacob  walked  9  miles  and  rode  7 ;  how 
far  did  he  go  ?  , 

8.  In  a  certain  class  there  are  7  boys  and  7, 
girls ;  how  many  pupils  are  there  in  the  class  ?' 

9.  Jeremiah  found  5  quills,  and  John  found 
7 ;  how  many  did  both  find  ? 

10.  In  a   certain  recitation  there  were  11 
questions  correctly  answered,  and  7  incorrectly 
answered ;  how  many  questions  were  asked  ? 


16 


ADDITION. 


LESSON    XIII. 


1. 

2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 

11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 


How  many  are  8 

How  many  are  8 

How  many  are  8 

How  many  are  8 

How  many  are  8 

How  many  are  8 

How  many  are  8 

How  many  are  8 

How  many  are  8 

How  many  are  8 

8  and  2  are  how 

8  and  5  are  how 

8  and  3  are  how 

8  and  7  are  how 

8  and  4  are  how 

8  and  G  are  how 

8  and  9  are  how 

8  and  10  are  how 

8  and  8  are  how 

11  and  8  are  how 


and  1  1 

and  2? 

and  3  ? 

and  4? 

and  5  ? 

and  6  ? 

and  7? 

and  8  ? 

and  9  ? 

and  10  ? 

many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 


LESSON    XIV, 


1.  A  beggar  met  two  boys ;  one  gave  him  7 
cents,  and  the  other  gave  him  8  cents;   how 
many  cents  did  both  give  him  ? 

2.  A  man  bought  a  hat  for  5  dollars,  and  a 
vest  for  8  dollars ;  what  was  the  cost  of  both  ? 

3.  There  were  8  boys  sitting,  and  3  stand- 
ing ;  how  many  boys  were  there  in  all  ? 


ADDITION. 


17 


4.  Rachel  gave  her  teacher  8  pinks,  and  2 
roses  ;  how  many  flowers  did  she  give  her  ? 

5.  Barlow   caught   8  squirrels,  and  Benton 
caught  4 ;  how  many  did  both  catch  ? 

0.  If  we  learn  6  pages  this  week,  and  8  the 
next,  how  many  shall  we  learn  in  the  two  weeks  ? 

7.  If  in  one  field  there  are  8  sheep,  and  in 
another  9,  how  many  are  in  both  ? 

8.  Charles  caught  8  fish,  and  Matthew  caught 
8  ;  how  many  did  both  catch  ? 

9.  George  shot  10  pigeons,  and  James  shot 
8  ;  how  many  did  both  snoot  ? 

10.  If  one  insect  has  6  legs,  and  another  insect 
has  8,  how  many  legs  are  on  both  insects  ? 


LESSON    XV. 


1. 

How 

many 

are 

9 

and     1 

2 

2. 

How 

many 

are 

9 

and     2 

2 

3. 

How 

many 

are 

9 

and     3 

2 

4. 

How 

many 

are 

9 

and     4 

2 

5. 

How 

many 

are 

9 

and     5 

2 

6. 

How 

many 

are 

9 

and     6 

2 

7. 

How 

many 

are 

9 

and     7 

2 

8. 

ilow 

many 

are 

9 

and     8 

2 

9. 

How 

many 

are 

9 

and     9 

2 

10. 

How 

many 

are 

9  • 

and  10 

11. 

9     and 

3 

are 

how 

many  ? 

12. 

9     and 

5 

are 

how 

many  ? 

13. 

7     and 

9 

are 

how 

many  2 

14.      9     and     9 

are 

how 

many  ? 

15. 

9     and    4 

are 

how 

many  ? 

18  ADDITION. 

16.  9  and     6     are    how  many  ? 

17.  8  and     9     are    how  many  2 

18.  9  and     2     are    how  many  ? 

19.  9  and  10     are     how  many  ? 

20.  9  and  11     are    how  many  ? 


LESSON    XVI. 

1.  Two  boys,  John  and  James,  gave  some 
money  to  a  beggar ;   John  gave  him  9  cents, 
and  James  gave  him  4  cents ;  how  many  cents 
did  both  give  him  ? 

2.  Gave  6  cents  to  Henry,  and  9  cents  to 
Hiram ;  how  many  cents  were  given  to  both  ? 

3.  Gave  7  nuts  to  one  boy,  and  9  to  another ; 
how  many  nuts  did  both  receive  ? 

4.  Bought  strawberries  for  9  cents,  and  plums 
for  5  cents ;  what  did  both  cost  ? 

5.  Bought  a  knife  for  11  cents,  and  a  whistle 
for  9  cents  ;  what  was  the  cost  of  both  ? 

6.  Gave  10  cents  for  an  arithmetic,  and  9 
cents  for  a  slate  ;  what  did  joth  cost  ? 

7.  Euphemia  learned  9  lessons,  and  Maria 
learned  8  ;  how  many  did  both  learn  I 

8.  A  boy  bought  raisins  for  9  cents,  and  a 
cake  for  3  cents ;  what  was  the  whole  cost  ? 

9.  A  lady  bought  some  tape  for  9  cents,  and 
some  thread  for  2  cents ;   how  much  did  both 
cost? 

10.  Gave  12  dollars  for  a  cow,  and  9  dollars 
for  a  sheep  ;  what  was  given  for  both  ? 


ADDITION.  19 


LESSON    XVII, 

1.  How    many  are  10     and     1  ? 

2.  How    many  are  10     and     2  ? 

3.  How     many  are  10     and     3  ? 

4.  How    many  are  10     and     4? 

5.  How     many  are  10     and     5  ? 

6.  How     many  are  10     and     6  ? 

7.  How    many  are  10     and     7  ? 

8.  How    many  are  10     amd     8  ? 

9.  How    many  are  10     and     9  ? 

10.  How    many  are  10     and  10  ? 

11.  3     and     10  are  how     ma»y  ? 

12.  5     and     10  are  how     many  ? 

13.  10     and       2  are  how     many  ? 

14.  10     and       4  *'  are  how     many  ? 

15.  8     and     10  are  how     many  ? 

16.  9     and     10  are  how     many  ? 

17.  10     and       6  are  how     many  ? 

18.  10     and     10  are  how     many  ? 

19.  10     and       7  are  how     many  ? 

20.  10     and     11  are  how     many  ? 

21.  How    many  are  11     and       2  ? 

22.  How     many  are  11     and       5  ? 

23.  How    many  are  6     and     11  ? 

24.  How     many  are  11     and       3  ? 

25.  How    many  are  1 1     and       4  ? 

26.  How    many  are  11     and       7  ? 

27.  How     many  are  9     and     11  ? 

28.  How     many  are  11     and     10  ? 

29.  How    many  are  11     aaxl     12  ? 

30.  How    many  are  11     and     14  ? 


20  ADDITION. 


LESSON     XVIII. 

1.  Mary  bought  a  pencil  for  6  cents,  a  book 
for  8  cents,  and  a  slate  for  10  cents ;  how  much 
did  all  cost  ? 

2.  Joseph  had  3  marbles,  John  6,  and  James 
10  ;  how  many  did  all  have  ? 

3.  Bought  a  cow  for  M  dollars,  and  a  calf 
for  6  dollars  ;  what  did  both  cost  ? 

4.  Bought  a  bottle  of  ink  for  6  cents,  some 
paper  for  5  cents,  and  some  pens  for  10  cents; 
what  was  paid^for  all  ? 

5.  Susan  is  11  years  old,  and  Nancy  is  9; 
what  is  the  sum  of  their  ages  ? 

6.  If  a  pound  of  beef  cost  8  cents,  and  a 
pound   of  pork  11  cents,  what   did  the   two 
pounds  cost? 

7.  A  lady  bought  pins  for  11  cents  and  rib- 
bon for  7  cents  ;  what  was  the  whole  cost  ? 

8.  B  sold  9  cows  to  one  man,  and  7  cows  to 
another ;  how  many  did  he  sell  to  both  ? 

9.  A  drover  bought  4  cows  of  one  man,  6  of 
another,  and  11  of  another;  how  many  did  he 
buy? 

10.  A  boy  gave  10   cents   for  a  whistle,  8 
cents  for  a  whip,  and  6  cents  for  a  top ;   how 
much  did  he  give  for  all  ? 

11.  A  merchant  sold  12  barrels  of  flour  one 
week,  and  8  the  next  week  ;  how  many  barrels 
did  he  sell  during  the  two  weeks  ? 

12.  A  farmer  bought  sugar  for  M  dollars, 
and  molasses  for  6  dollars ;  what  cost  both  ? 


ADDITION.  21 

13.  Simeon  gave  8  cents  for  a  melon,  6  cents 
for  a  pine-apple,  and  had  6  cents  remaining; 
how  much  had  he  at  first  ? 

14.  Abner  found  12  eggs,  and  Alice  found 
10 ;  how  many  did  both  find  ? 

15.  A  boy  saw  7  pigeons  on  one  tree,  8  on 
another,  and  5  on  another ;  how  many  did  he 
see  in  all  ? 

16.  A  man  bought  a  watch  for  15  dollars, 
and   had   ten   dollars   remaining;   how  many 
dollars  had  he  at  first  ? 

17.  Egbert  gave  4:  cherries  to  Oliver,  7  to 
Edwin,  and  kept  12  himself;   how  many  had 
he  at  first  ? 

18.  Elizabeth  picked  8  quarts  of  blackberries, 
Ellen  5  quarts,  and  Helen  7  quarts ;  how  many 
quarts  did  all  pick  ? 

19.  Samuel  gave  2  dimes  for  his  breakfast,  4 
dimes  for  his  dinner,  and  had  14  dimes  left; 
how  much  had  he  at  first  ? 

20.  A  boy  traveled   14:  miles  one  day,  and 
11  the  next;  how  far  did  he  travel  in  the  two 
days? 

21.  Henry  gave  4  roses  to  Anna,  6  roses  to 
Mary,  and  had  5  roses  remaining ;  how  many 
ros^fe  had  Henry  at  first  ? 

22.  James  picked  six  quarts  of  blackberries, 
John  picked  8  quarts,  and  Maggie  picked  12 
quarts ;  how  many  quarts  did  all  pick  ? 

23.  Moses  bought  7  marbles  of  John,  9  of 
Albert,  and  11  of  Jaekson;  how  many  did  he 
buy  in  all  ? 


SUBTRACTION. 


LESSON    I. 

1.  3  less  1  are  how  many ! 
ANALYSIS. — Three  less  one  are  two. 

2.  4:  less  1  are  how  many  ? 

3.  5  less  1  are  how  many  ? 

4.  6  less  1  are  how  many  ? 

5.  7  less  1  are  how  many  ? 

6.  8  less  1  are  how  many  ? 

7.  9  less  1  are  how  many  ? 

8.  10  less  1  are  how  many  ? 

9.  3  less  2  are  how  many  ? 

10.  4  less  2  are  how  many  ? 

11.  5  less  2  are  how  many  ? 

12.  6  less  2  are  how  many  ? 

13.  7  less  2  are  how  many  ? 

14.  8  less  2  are  how  many  ? 

15.  9  less  2  are  how  many  ? 

16.  10  less  2  are  how  many  ? 

17.  4  less  3  are  how  many  ? 

18.  5  less  3  are  how  many  ? 

19.  6  less  3  are  how  many  ? 

20.  7  less  3  are  how  many  ? 

21.  8  less  3  are  how  many  ? 

22.  9  less  3  are  how  many  ? 

23.  10  less  3  are  how  many  ? 

24.  4  less  4  are  how  many  ? 

25.  5  less  4  arve  how  many  ? 


SUBTRACTION.  23 


LESSON    II. 

1.  If  I  have  3  apples,  and  give  1  of  them  to 
James,  liow  many  have  I  left  ? 

ANALYSIS. — If  I  have  3  apples,  and  give  1  of  them  to 
James,  I  will  have  remaining  the  difference  between  3 
apples  and  1  apple,  which  is  2  apples. 

2.  A  boy  had  4  chestnuts,  and  gave  1  away ; 
how  many  had  he  left  ? 

3.  Catharine  had  6  pins,  and  gave  1  away ; 
how  many  had  she  left  ? 

4.  Rebecca  bought  6  cakes,  and   ate  2  of 
them ;  how  many  had  she  left  ? 

5.  Rachel  had  4  apples,  and  gave  2  of  them 
to  George ;  how  many  had  she  left  ? 

6.  Alice  bought  5  cakes,  and  ate  3  of  them 
for  her  dinner ;  how  many  had  she  left  ? 

7.  Agnes  had  6  quarts  of  berries,  and  sold  2 
quarts  of  them ;  how  many  had  she  remaining? 

8.  Anna  had  5  books,  and  lost  three  of  them ; 
how  many  had  she  remaining  ? 

9.  Weston  had  6  marbles,  and  gave  2  of  them 
to  John  ;  how  many  had  he  remaining  ? 

10.  Eliza  had  8  oranges,  and  gave  her  sister 
2  of  them  ;  how  many  had  she, remaining  ? 

11.  Sarah  had  9  pinks,  and  gave  lier  teacher 
2  of  them ;  how  many  had  she  left  1 

12.  Isaac  saw  10  pigeons  on  a  tree ;   2  of 
them  flew  away ;  how  many  remained  ? 

13.  David  had  6  apples,  and  gave  3  to  his 
brother  ;  how  many  had  he  remaining  ? 

14  Sold  some  apples  for  9  cents,  and  some 


24  SUBTRACTION. 

pears  for  4:  cents ;   how  mucli  more  did  I  get 
for  the  apples  than  for  the  pears  ? 

15.  Louise  had  8  roses,  and  gave  4  of  them 
to  Ann ;  how  many  had  she  remaining  ? 

16.  Walter  gave  9  cents  for  a  book,  and  4 
cents  for  a  pencil;    how  much  more  did  the 
book  cost  than  the  pencil  ? 

17.  A  farmer  sold  a  calf  for  12  dollars,  and 
a  sheep  for  4  dollars  ;  how  much  more  did  he 
receive  for  the  calf  than  for  the  sheep  ? 

18.  Jane  is  10  years  old,  and  Susan  is  6; 
how  many  years  older  than  Susan  is  Jane  ? 

19.  Mary  found  12  quills,  and  lost  5  of  them ; 
how  many  had  she  remaining  ? 

20.  Pamela  gave  13  cents  for  a  comb,  and  9 
cents  for  some  tape ;  how  much  more  did  the 
comb  cost  than  the  tape  ? 


LESSON  III. 

1.  5  less  5  are  how  many  ? 

2.  6  less  5  are  how  many  ? 

3.  7  less  5  are  how  many  ? 

4.  8  less  5  are  how  many  ? 

5.  9  less  5  are  how  many  ? 

6.  10  less  5  are  how  many  ? 

7.  12  less  5  are  how  many  ? 

8.  6  less  6  are  how  many  ? 

9.  7  less  6  are  how  many  ? 

10.  8  less  6  are  how  many? 

11.  9  less  6  are  how  many  ? 

12.  10  less  6  are  how  many  ? 


SUBTRACTION.  25 

13.  11  less  6  are  how  many  ? 

14.  6  less  3  are  liow  many  ? 

15.  7  less  5  are  how  many  ? 

16.  10  less  7  are  how  many  ? 

17.  9  less  7  are  how  many  ? 

18.  8  less  5  are  how  many  ? 
1Q.  12  less  7  are  how  many  ? 

20.  14  less  6  are  how  many  ? 

21.  12  less  2  are  how  many  ? 

22.  13  less  3  are  how  many  ? 

23.  14  less  4  are  how  many  ? 

24.  15  less  5  are  how  many  ? 

25.  12  less  9  are  how  many  ? 

26.  12  less  10  are  how  many  ? 

27.  12  less  7  are  how  many  ? 

28.  12  less  5  are  how  many  ? 

29.  9  less  7  are  how  many  ? 

30.  13  less  7  are  how  many  ? 


LESSON    IV. 

1.  Edward  had  9  oranges,  and  gave  5  of  them 
to  his  sister;  how  many  "had  he  left? 

2.  A  boy  had  11  rabbits,  3  of  which  were 
killed  by  a  dog ;  how  many  had  he  left  ? 

3.  A  farmer,  having  8  bushels  of  apples,  sold 
5  bushels  of  them ;  how  many  were  left  ? 

4.  A  boy  had  9  birds  and  4  squirrels;  how 
many  more  birds  had  he  than  squirrels ; 

5.  There  were  15  questions  asked  during  a 
recitation,  5  of  which  were  answered    incor- 
rectly; how  many  were  correctly  answered  ? 


ZO  8UBTBAOTION. 

6.  Julia,  finding  14  roses  on  her  bush,  picked 
off  5 ;  how  many  remained  on  the  bush  '( 

7.  There  were  7  passengers  in  a  stage,  3  of 
whom  got  out ;  how  many  remained  in  ? 

8.  A  boy,  having  6  cents,  spent  2  cents  for 
candies;  how  many  cents  had  he  remaining ? 

9.  Henry  bought  8  quill  pens,  and  used  3  of 
them  in  a  week ;  how  many  remained  unused  ? 

10.  George  sold  some  marbles  for  11  cents, 
which  was  4  cents  more  than  their  cost ;  what 
was  their  cost  ? 

11.  A  merchant  bought  sugar  for  14  dollars, 
and  sold  it  for  11  dollars;  how  much  did  he 
lose? 

12.  "Walter  gave  14  cents  for  a  slate,  and  4 
cents  for  a  sponge ;  how  much  more  did  the 
slate  cost  than  the  sponge  ? 

13.  Bought  a  book  for  8  cents,  and  sold  it  for 
11  cents ;  how  many  cents  did  I  gain  ? 

14.  Bought  a  book  for  10  cents,  and  sold  it 
for  15  cents ;  how  many  cents  did  I  gain  ? 

15.  James  bought  a  pair  of  boots  for  7  dol- 
lars, and  handed  the  shopkeeper  a  1(5  dollar 
bill ;  how  much  ought  he  to  receive  back  ? 

16.  Jacob  bought  a  sled  for  15  cents,  and 
sold  it  for  9  cents  ;  how  much  did  he  lose  ? 

17.  If  8  boys  are  taken  out  of  a  class  of  18 
boys,  how  many  boys  will  there  be  left  ? 

18.  A  lady  bought  17  eggs,  and  broke  7  of 
them ;  how  many  "had  she  left  ? 

19.  If  a  window  have  16  panes  of  glass,  and 
7  of  them  are  broken,  how  many  whole  panes 
will  be  left? 


MULTIPLICATION. 


LESSON 

I. 

TABLE 

. 

2 

times  1 

are 

2. 

3 

times  1 

are 

3. 

2 

u 

2 

« 

4. 

3 

a 

2 

a 

6. 

2 

u 

3 

a 

6. 

3 

a 

3 

a 

9. 

2 

(1 

4 

tt 

8. 

3 

« 

4 

a 

12. 

2 

u 

5 

a 

10. 

3 

a 

5 

u 

15. 

2 

« 

6 

a 

12. 

3 

a 

6 

a 

18. 

2 

« 

7 

U 

14. 

3 

" 

7 

" 

21. 

2 

a 

8 

a 

16. 

3 

a 

8 

a 

24. 

2 

u 

9 

a 

18. 

3 

« 

9 

a 

27. 

2 

« 

10 

a 

20. 

3 

a 

10 

a 

30. 

2 

u 

11 

a 

22. 

3 

a 

11 

a 

33. 

2 

H 

12 

a 

24. 

3 

a 

12 

" 

36. 

1.      How    many     are     2     times     2  ? 
ANALYSIS. — Two  tiines  two  are  four. 


2. 

How 

many 

are 

two 

timos 

4V 

3. 

How 

many 

are 

two 

times 

8? 

4. 

How 

many 

are 

two 

times 

3? 

5. 

How 

many 

are 

two 

times 

5  ? 

6. 

How 

many 

are 

two 

times 

7? 

7. 

How 

many 

are 

two 

times 

91 

8. 

How 

many 

are 

two 

times 

7? 

9. 

How 

many 

are 

two 

times 

11? 

10. 

How 

many 

are 

two 

times 

10? 

11. 

How 

many 

are 

two 

times 

12? 

28 


MU  LTIPLIC  ATION. 


12. 

How 

many 

are 

three 

times 

4? 

13. 

How 

many 

are 

three 

times 

2? 

14. 

How 

many 

are 

three 

times 

3? 

15. 

How 

many 

are 

three 

times 

5? 

16. 

How 

many 

are 

three 

times 

8? 

17. 

How 

many 

are 

three 

times 

7? 

18. 

How 

many 

are 

three 

times 

10? 

19. 

How 

many 

are 

three 

times 

12? 

20. 

How 

many 

are 

three 

times 

11  ? 

21. 

How 

many 

are 

three 

times 

6  ? 

22. 

How 

many 

are 

.»  «.  »  — 

three 

times 

9? 

LESSON    II, 

1.  What  cost  2  lemons,  at  4  cents  each? 

ANALYSIS. — If  1  lemon  cost  4  cents,  2  lemons  will 
cost  two  times  4  cents,  which  are  8  cents. 

2.  What  cost  2  apples,  at  4  cents  each  ? 

3.  What  cost  2  peaches,  at  3  cents  each  ? 

4.  What  cost  2  caps,  at  5  dimes  each  ? 

5.  What  cost  3  melons,  at  11  cents  each  ? 

6.  What  cost  3  books,  at  12  cents  each  ? 

7.  What  cost  2  slates,  at  9  cents  each  ? 

8.  What  cost  2  pencils,  at  6  cents  each  ? 

9.  What  cost   2  pounds  of  raisins,  at  12 
cents  a  pound  ? 

10.  What  cost  3  pine-apples,  at  9  cents  each? 

11.  What  cost  3  lamps,  at  4  dimes  each  ? 

12.  What  cost  3  looking-glasses,  at  6  dimes 
each  ? 

13.  What  cost  3  writing-books,  at  3  dimes 
each? 


MULTIPLICATION. 


29 


14:.  "What  cost  3   candlesticks,  at  5  dimes 

each? 

15.  "What  cost  3  inkstands,  at  7  cents  each? 

16.  What  cost  2  balls  of  tape,  at  10  cents  a 
ball? 

17.  What  cost  2  hammers,  at  11  cents  each? 

1 8.  What  cost  3  papers  of  needles,  at  8  cents 
a  paper  ?- 

19.  What  cost  2  baskets  of  strawberries,  at  7 
cents  a  basket  ? 


LESSON    III, 


TABLE. 


4  times  1  are     4. 

4.     «       2     " 
4     "       3     " 

« 

u 


1.  Four  times  3  are  how  many  ? 

2.  Four  times  6  are  how  many  ? 

3.  Four  times  8  are  how  many  ? 

4.  Four  times  7  are  how  many  ? 

5.  Four  times  4  are  how  many  ? 

6.  Four  times  2  are  how  many  ? 


4 

a 

4 

4 

u 

5 

4 

" 

6 

4 

a 

7 

4 

u 

8 

4 

a 

9 

4 

a 

10 

4 

" 

11 

4 

u 

12 

4. 

5 

times  1 

are 

5. 

8. 

5 

u 

2 

" 

10. 

12. 

5 

" 

3 

" 

15. 

16. 

5 

u 

4 

u 

20. 

20. 

5 

u 

5 

a 

25. 

24. 

5 

u 

6 

a 

30. 

28. 

5 

u 

7 

u 

35. 

31 

5 

" 

8 

a 

40. 

36. 

5 

u 

9 

« 

45. 

40. 

5 

" 

10 

a 

50. 

41. 

5 

u 

11 

tt 

55. 

48. 

5 

« 

12 

a 

60. 

30 


MULTIPLICATION. 


7. 

Four 

times 

11 

are 

how 

many  ? 

8. 

Five 

times 

3 

are 

how 

many  ? 

9. 

Five 

times 

5 

are 

how 

many  ? 

10. 

Five 

times 

4 

are 

how 

many  ? 

11. 

Five 

times 

6 

are 

how 

many  ? 

12. 

Four 

times 

10 

are 

how 

many  ? 

13. 

Five 

times 

2 

are 

how 

rnjfaiy  ? 

14. 

Four 

times 

2 

are 

how 

many  ? 

15. 

Five 

times 

9 

are 

how 

many  ? 

16. 

Five 

times 

8 

are 

how 

many  ? 

17. 

Five 

times 

10 

are 

how 

many  ? 

18. 

Four 

times 

11 

are 

how 

many  ? 

19. 

Five 

times 

11 

are 

how 

many  ? 

20. 

Four 

times 

12 

are 

how 

many  ? 

21. 

Five 

times 

12 

are 

how 

many  ? 

LESSON    IV. 

1.  What  cost  4  pairs  of  shoes,  at  3  dollars  a 
pair  ? 

2.  What  cost  5  pounds  of  mutton,  at  6  cents 
a  pound  ? 

3.  What  cost  4  barrels  of  sugar,  at  8  dollars 
a  barrel  ? 

4.  What  cost  5  pounds  of  sturgeon,  at  10 
cents  a  pounds  ? 

5.  Wh^it  cost  4  pounds  of  almonds,  at  11 
cents  a  pound  ? 

6.  What  cost  5  barrels  of  pork,  at  9  dollars  a 
barrel  ? 

7.  What  cost  4  pounds  of  candles,  at  10  cents 
a  pound  ? 


MULTIPLICATION.  Si 

8.  What  cost  5  coats,  at  4  dollars  each  ? 

9.  "What  cost  4  handkerchiefs,  at  5  dimes 
each? 

10.  What  cost  5  lamps,  at  3  dimes  each  ? 

11.  What  cost  4  plows,  at  7  dollars  each? 

12.  What  cost  5  boxes  of  caps,  at  11  cents  a 
box  ? 

13.  What  cost  4  quires  of  paper,  at  12  cents 
a  quire  ? 

14.  What  cost  5  letter-folders,  at  11  cents 
each  ? 

15.  What  cost  4  oranges,  at  7  cents  each? 

16.  What   cost   5   pen-knives,   at   12   cents 
each  ? 

17.  What   cost  4  bunches  of  grapes,  at  9 
cents  a  bunch  ? 

18.  What    cost    5    pine-apples,    at    8    cents 
each? 

19.  What  cost  4  spools  of  cotton,  at  6  cents 
each? 

20.  What  cost  5  pounds  of  ginger,  at  7  cents 
a  pound  ? 


L 

ESSON 

V. 

TABLE. 

6 

times 

1 

are 

6. 

6 

tim 

f> 

44 

2 

44 

12. 

6 

44 

p> 

u 

[j 

44 

18. 

6 

44 

(3 

44 

4 

44 

24. 

6 

" 

6 

44 

5 

44 

30. 

6 

44 

6 

44 

fl 

44 

36. 

6 

a 

8  "  48. 

9  "  54. 

10  "  CO. 

11  "  66. 

12  "  72, 


MULTIPLICATION. 


7  times  1  are  7. 
7  "  2  "  14. 
"  3  "  21. 


" 


7 
7 
7    « 
7    " 

1. 

2. 
3. 

5! 

6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 

15.' 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 


4 
5 
6 


28. 
35. 
42. 


7  times  7  are  49. 

7    "      8  "     56. 

7    "      9  "     63. 

7    "     10  «     70. 
7    «    11 
7    "     12 


«    77. 
«    ftj. 


Six  times  2 
Six  times  5 
Seven  times 
Seven  times 
Six  times  8 
Six  times  7 
Six  times  10 
Seven  times 
Seven  times 
Seven  times 
Six  times  3 
Six  times  6 
Six  times  4 
Seven  times 
Seven  times 
Seven  times 
Six  times  9 
Six  times  12 
Six  times  21 
Seven  times 
Seven  times 
Seven  times 
Seven  times 
Seven  times 
Six  times  15 
Six  times  20 


are  how  many  ? 
are  how  many  ? 

5  are  how  many  ? 

2  are  how  many  ? 
are  how  many  ? 
are  how  many  ? 

are  how  many  ? 

7  are  how  many? 

8  are  how  many  ? 

10  are  how  many  ! 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 

6  are  how  many  2 

3  are  how  many  ? 

4  are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 

11  are  how  many  ? 
9  are  how  many  ? 

12  are  how  many  ? 

13  are  how  many  ? 
15  are  how  many  ? 

are  how  many  ? 
are  how  many  ? 


MULTIPLICATION.  83 


LESSON    VI. 

1.  What  cost  6  quarts  of  cherries,  at  4  cents 
a  quart  ? 

2.  What  cost  7  quarts  of  raspberries,  at  4 
cents  a  quart  ? 

3.  What  cost  6  lead  pencils,  at  5  cents  each  ? 

4.  What  cost  7  pens,  at  3  cents  each  ? 

5.  What  cost  7  lead  pencils,  at  5  cents  each  ? 

6.  What  cost  5  cakes,  at  3  cents  eacli  ? 

7.  What  cost  7  figs,  at  2  cents  each? 

8.  What  cost  5  pictures,  at  6  cents  each  ? 

9.  What  cost  5  tomatoes,  at  2  cents  each  ? 

10.  What  cost  6  ounces  of  cinnamon,  at  G 
cents  an  ounce  ? 

11.  What  cost  5  pounds  of  cheese,  at  8  cents 
a  pound  ? 

12.  What  cost  7  pounds  of  prunes,  at  9  cents 
a  pound  ? 

13.  What  cost  5  fish-hooks,  at  9  cents  each? 

14.  What  cost  7  yards  of  calico,  at  8  cents  a 
yard? 

15.  What  cost  G  skeins  of  silk,  at  8  cents  a 
skein  ? 

1G.  What   cost   G  pounds  of  starch,  at  12 
cents  a  pound  ? 

17.  What  cost  7  barrels  of  flour,  at  10  dol- 
lars a  barrel  ? 

18.  What  cost  G  bushels  of  potatoes,  at  9 
dimes  a  bushel  ? 

19.  What  cost  7  primers,  at  11  cents  each? 

20.  What  cost  7  coats,  at  12  dollars  each  ? 


34 


MULTIPLICATION. 


LESSON    VII. 


TABLE. 


8 

times  1 

are 

8. 

9 

times  1 

are     9. 

8 

ft 

2 

ft 

16. 

9 

ft 

2 

ft 

18. 

8 

ft 

3 

ft 

24. 

9 

ft 

3 

ft 

27. 

8 

ft 

4 

ft 

32. 

9 

" 

4 

ft 

36. 

8 

ft 

5 

ft 

40. 

9 

ft 

5 

ft 

45. 

8 

ft 

6 

ft 

48. 

9 

ft 

6 

ft 

54. 

8 

ft 

7 

ft 

56. 

9 

ft 

7 

ft 

63. 

8 

ft 

8 

ft 

64. 

9 

ft 

'8 

ft 

72. 

8 

ft 

9 

" 

72. 

9 

ft 

9 

ft 

81. 

8 

ft 

10 

ft 

80. 

9 

ft 

10 

ft 

90. 

8 

ft 

11 

ft 

88. 

9 

ft 

11 

ft 

99. 

8 

ft 

12 

" 

96.     J 

9 

ft 

12 

ft 

108. 

1.  Eight  times  4  are  how  many  ? 

2.  Eight  times  6  are  how  many  ? 

3.  Eight  times  3  are  how  many  ? 

4.  Eight  times  2  are  how  many  ? 

5.  Eight  times  5  are  how  many  ? 

6.  Nine  times  4  are  how  many  ? 

7.  Nine  times  3  are  how  many  ? 

8.  Nine  times  6  are  how  many  ? 

9.  Nine  times  5  are  how  many  ? 

10.  Nine  times  2  are  how  many  ? 

11.  Eight  times  12  are  how  many  ? 

12.  Nine  times  7  are  how  many  ? 

13.  Eight  times  11  are  how  many  ? 

14.  Nine  times  8  are  how  many  ? 

15.  Nine  times  10  are  how  many  ? 

16.  Eight  times  10  are  how  many  ? 


MULTIPLICATION.  35 

17.  Eight  times  9  are  how  mai^y? 

18.  Nine  times  11  are  how  many  ? 

19.  Eight  times  8  are  how  many  ? 

20.  Nine  times  12  are  how  many  ? 


LESSON    VIII, 

1.  "What  cost  9  sticks  of  tape,  at  4  cents  a 
stick  ? 

2.  What  cost  8  yards  of  calico,  at  12  cents  a 
yard  ? 

3.  What  cost  9  combs,  at  2  cents  each  ? 

4.  What    cost    8    pine-apples,   at   11   cents 
each  ? 

5.  What  cost  9  spools  of  thread,  at  11  cents 
a  spool  ?  I 

0.  What  cost  8  brushes,  at  10  cents  each  ?  * 

7.  What  cost  9  cakes  of  paint,  at  5  dimes  a 
cake  ? 

8.  What  cost  8  yards  of  muslin,  at  9  cents  a 
yard  ? 

9.  What  cost  9  citrons,  at  9  cents  each  ? 

10.  What  cost  8  boxes  of  caps,  at  8  cents  a 
box? 

11.  What  cost  9  oranges,  at  6  cents  each? 

12.  What  cost  8  boxes  of  figs,  at  7  dimes  a 
box? 

13.  What  cost  9  lemons,  at  7  cents  each? 
H.  What  cost  9  feet  of  boards,  at  8  cents  a 

foot  ? 

15.  What  cost  9  bushels  of  oats,  at  11  cents 
a  bushel  ? 


36 


MULTIPLICATION. 


16.  What  cost  8  yards  of  merino,  at  3  dimes 
a  yard  ? 

17.  What  cost  9  yards  of  broadcloth,  at  5 
dollars  a  yard  ? 

18.  What  cost  9  plows,  at  10  dollars  each? 

19.  What  cost  8  chickens,  at  5  cents  each? 

20.  What  cost  9  pigeons,  at  12  cents? 


LESSON  IX. 


TABLE. 


10 

times  1 

are  10. 

11 

times  1 

are  11. 

10 

u 

2 

« 

20. 

11 

a 

2 

K 

22. 

10 

a 

3 

ct 

30. 

11 

a 

3 

u 

33. 

10 

a 

4 

u 

40. 

11 

a 

4 

a 

44. 

10 

a 

5 

u 

50. 

11 

u 

5 

U 

55. 

10 

u 

6 

u 

60. 

11 

a 

6 

(C 

(56. 

10 

« 

7 

u 

70. 

11 

a 

7 

u 

77. 

10 

a 

8 

u 

80. 

11 

u 

8 

a 

88. 

10 

a 

9 

a 

90. 

11 

a 

9 

a 

99. 

10 

u 

10 

a 

100. 

11 

a 

10 

u 

110. 

10 

« 

11 

a 

no. 

11 

a 

11 

a 

121. 

10 

« 

12 

a 

120. 

11 

U 

12 

« 

132. 

LESSON  X. 

4-     1.  If  a  boy  travel  5  miles  in  one  day,  how 
far  will  he  go  in  10  days  ? 

2.  If  a  boy  earn  5  cents  a  day,  how  many 
centp  will  he  earn  in  11  days? 

3.  If  James  has  3  marbles,  and  John  has  11 
times  as  many,  how  many  has  he  ? 


MULTIPLICATION.  37 

4.  If  a  hare  run  three  rods  in  a  second,  how 
far  will  she  run  in  10  seconds  ? 
t  5.  Jacob  is  7  years  old,  and  Josiah  is  11  times 
as  old  as  Jacob ;  how  old  is  Josiah  ? 

6.  If  I  pay  7  cents  for  riding  one  mile,  how 
much  must  I  pay  for  riding  10  miles  ? 

7.  Mary  has  2  roses,  and  Sarah  has  10  times 
as  many  ;  how  many  has  she  ? 

jy  8.  Albert  killed  2  birds,  and  saw  11  times  as 
many  more ;  how  many  did  he  see  ? 

9.  Eachel  has  4  pins,  and  George  10  times 
as  many  ;  how  many  has  he  ? 

10.  Moses  gave  4  cents  for  a  piece  of  pie ; 
what  would  11  pieces  cost  at  the  same  rate  ? 

11.  If  a  stage-coach  go  6  miles  in  one  hour, 
far  will  it  go  in  11  hours  ? 

12.  If  a  man  shear  6  sheep  in  one  day,  how 
many  can  he  shear  in  10  days  ? 

13.  Henry  is  worth  8  dollars,  and  Hiram  is 
worth  11  times  as  much ;  how  much  is  Hiram 
worth  ? 

14.  What  will  8  tons  of  hay  cost,  at  10  dol- 
lars a  ton  ? 

J  15.  What  will  9  firkins  of  butter  cost,  at  11 
dollars  a  firkin  ? 

16.  What  will  9  pounds  of  fish  cost,  at  11 
cents  a  pound  ? 

17.  Munson  caught  10  fish,  and  Marvin  10 
times  as  many ;  how  many  did  Marvin  catch  ? 

18.  What  cost  11  quarts  of  walnuts,  at  10 
cents  a  quart? 

19.  A  farmer  sold  11  cattle,  at  11  dollars 
each ;  what  did  he  receive  for  them  all  ? 

4 


3  8  MULTIPLICATION. 

LESSON    XI. 

TABLE. 


12 

times 

1 

are 

12. 

12 

u 

2 

u 

24 

12 

(4 

3 

u 

36. 

12 

It 

4 

u 

48. 

12 

« 

5 

u 

GO. 

12 

a 

G 

u 

72. 

12 

a 

7' 

a 

84. 

12 

a 

8 

a 

9G. 

12 

a 

9 

u 

108. 

12 

it 

10 

u 

120. 

12 

a 

11 

u 

132. 

12 

u  , 

12 

u 

144. 

1.  How  many  are  12  times  3  ? 

2.  How  many  are  12  times  5  ? 

3.  How  many  are  12  times  4  ? 

4.  How  many  are  12  times  2  ? 

5.  How  many  are  12  times  G  ? 
G.  How  many  are  12  times  7  ? 

7.  How  many  are  12  times  9  ? 

8.  How  many  are  12  times  11  ? 

9.  How  many  are  12  times  12  ? 
10.  How  many  are  12  times  10  ? 

Twelve  times  8  are  how  many  ? 

Twelve  times  12  are  how  many  ? 

Twelve  times  7  are  how  many  ? 

Twelve  times  11  are  how  many  ? 

Twelve  times  5  are  how  many  ? 

Twelve  times  9  are  how  in  any  ? 

Twelve  times  6  are  how  many  ? 


MULTIPLICATION.  39 

LESSON    XII. 

1.  In  a  certain  school  there  were  8  girls,  and 
12  times  as  many  boys ;  how  many  boys  were 
there  in  the  school  ? 

ANALYSIS. — If  in  the  school  there  are  8  girls,  and  12 
times  as  many  boys,  there  must  be  13  times  8  boys, 
which  are  96  boys. 

2.  In  a  school-room  are  12  benches,  and  9 
boys  on  each  bench ;  how  many  boys  in  the 
school  ? 

3.  In  a  corn-field  are  12  rows,  and  12  hills 
in  each  row  ;  how  many  hills  in  the  field  ? 

4.  Bought  5  pounds  of  beef  at  6  cents  a 
pound,  and  8  pounds  of  rice  at  5  cents  a  pound ; 
what  was  the  whole  cost  ? 

5.  A's  house  is  5  rods  from  the  meeting- 
house, B's  is  3  times  as  far  as  A's,  and  C's  is 
twice  as  far  as  B's ;   how  far  are  B's  and  O's 
houses  from  the  meeting-house  ? 

6.  A  farmer  sold  11  bushels  of  potatoes,  and 
had  12  times  as  many  bushels  remaining ;  how 
many  bushels  had  he  remaining  ? 

7.  In  a  school-room  are  12  rows  of  seats,  and 
9  seats  in  each  row ;  how  many  seats  are  there? 

8.  "What  cost  8  pounds  of  chocolate,  at  12 
cents  a  pound  ? 

9.  A  boy  earned  35  cents  a  day,  and  paid  25 
cents  a  day  for  his  board ;  how  much  had  he 
left  at  the  expiration  of  6  days  ? 

10.  A  farmer  bought  9  acres  of  land,  at  11 
dollars  an  acre ;  what  did  it  all  cost  ? 


MULTIPLICATION. 


NOTE. — The  sign  of  Multiplication  is  X,and  is  read,  multiplied  5y,  or 
times.    The  sign  of  Equality  is  =,  and  is  read  equals,  or  equal  to. 


Ix   1=     1 

Ix    2=     2 

Ix    3=     3 

Ix    4=     4 

2X      1  =        2 

2x    2=     4 

2x    3=     6 

2x   4=     8 

3x    1=     3 

3x    2=     6 

3x    3=     9 

3x   4=  12 

4x    1=:     4 

4x    2=     8 

4x    3=    12 

4x   4=  16 

5x    1  =     5 

5x    2=  10 

5x    3=    15 

5x   4=  20 

6x    1=     6 

6x    2=  12 

6x    3=   18 

6x   4=  24 

7x    1=     7 

7x    2=  14 

7x    3=   21 

7x   4=  28 

8x    1=     8 

8x    2=  16 

8x    3=  24 

8x  4=  32 

9x1  =     91  9x    2=  18 

9x    3=  27 

9x   4=  36 

10  x    1  =  lOilOx    2=  20 

10  x    3=   30 

10  x   4=  40 

11  x    1=  11  jllx    2=  22 

11  x    3=   33  |llx   4=  44 

12  x    1=  12  J12x    2=  24 

12  x    3=  36  |!2x   4=  48 

Ix    5=     5     Ix    6=     6 

Ix    7=     7 

Ix   8=     8 

2x    5=  10     2x    6  =   12 

2x    7=  14 

2x    8=  16 

3x   5=  15 

3x    6=   18 

3x    7=  21 

3x    8=  24 

4x    5=  20     4x    C=   24 

4x    7=  28 

4x    8=  32 

5x   5=  25     5x    6  =   30 

5x    7=  35 

5x   8=  40 

6x    5=  30     6x    6=    36 

6x    7=  42 

6x    8=  48 

7  x   5=  35  i  Vx    6=   42 

7x    7=  49 

7x   8=  56) 

8x    5=  40 

8x    6=   48 

8x    7=  56 

8x    8=  64 

9x    5=  45 

9x    6=    54 

9x    7=  63 

9x   8=  72 

10  x    5:=  50 

10  x    6=   60 

10  x    7=  70  10  x    8=  80 

11  x    5=  55  11  x    6=    60 

11  x    7=  77  ill  x    8=  88 

12  x    5=  60  112  x    6=   72 

12  x    7=  8412x   8=  96 

1x9=     9 

1x10=   10 

1x11=   11 

1x12=  12 

2x    9=  18 

2x10=  20 

2x11=  22 

2x12=  24 

3x    9=  27 

3x10=  30 

3x11=   33 

3x12=  36 

4x    9=  36 

4x10=  40 

4x11=  44 

4x12=  48 

5x    9=  45 

5x10=  50 

5x11=   55 

5x12=  60 

6x    9=  54 

6x10=  60 

6x11=   66 

6x12=  72 

7x    9=  63 

7x10=  70 

7x11=   77 

7x12=  84 

8x    9=  72 

8x10=  80 

8x11=   88 

8x12=  96 

9x    9=  81 

9x10=  90 

9x11=   99 

9x12=108 

10  x    9=  90 

10x10=100 

10x11  =  110 

10x12=120 

11  x    9=  99  11x10=110 

11x11  =  121 

11x12=132 

12  x    9=108  |l2x  10=120 

12x11  =  132 

12x12=144 

DIVISION. 


LESSON    I. 


1. 

4: 

are 

how 

many 

times 

2? 

ANALYSIS.  —  4 

are 

as  many  times  2, 

as  2  is  contained 

times  in 

4,  whic 

U  are 

2  times. 

2. 

2 

are 

how 

many 

times 

2? 

3. 

6 

are 

how 

many 

times 

2? 

4 

8 

are 

how 

many 

times 

2? 

5. 

10 

are 

how 

many 

times 

2? 

6. 

12 

are 

how 

many 

times 

2? 

:  7. 

14 

are 

how 

many 

times 

2? 

8. 

16 

are 

how 

many 

times 

2? 

9. 

3 

are 

how 

many 

times 

31 

10. 

9 

are 

how 

many 

times 

3? 

11. 

6 

are 

how 

many 

times 

3? 

12. 

12 

are 

how 

many 

times 

3? 

13. 

15 

are 

how 

many 

times 

3? 

14 

18 

are 

how 

many 

times 

3? 

15. 

21 

are 

how 

many 

times 

3? 

16. 

18 

are 

how 

many 

times 

2? 

17. 

20 

are 

how 

many 

times 

2? 

18. 

22 

are 

how 

many 

times 

21 

LESSON    II, 

1.  If  I  give  for  one  apple  2  cents,  how  many 
apples  can  I  buy  for  4  cents  ? 

ANALYSIS. — If  for  2  cents  I  can  buy  1  apple,  for  4 
cents  I  can  buy  as  many  apples  as  2  is  contained  times 
in  4,  which  are  2  times.  Therefore,  at  2  cents  each,  for 
4  cents  I  can  buy  2  apples. 


42  DIVISION. 

2.  At  2  cents  each,  how  many  pears  can  I 
buy  for  6  cents  ? 

3.  At  2  cents  each,  how  many  oranges  can  I 
buy  for  8  cents  ? 

4.  At  three  dimes  a  yard,  how  many  yards 
of  calico  can  be  had  for  12  dimes  ? 

5.  At  3  cents  each,  how  many  lemons  can  be 
had  for  9  cents  ? 

6.  At  2  cents  a  yard,  how  many  yards  of 
tape  can  be  bought  for  10  cents  ? 

7.  At  two  dimes  a  bushel,  how  many  bushels 
of  apples  may  be  had  for  12  dimes  ? 

8.  How  many  baskets  of  strawberries,  at  3 
cents  a  basket,  can  be  had  for  15  cents  ? 

9.  How  many  pounds  of  ginger,  at  2  dimes 
a  pound,  may  be  had  for  14  dimes  ? 

10.  For  18  dollars,  how  many  yards  of  cloth 
can  be  had,  at  2  dollars  a  yard  ? 

11.  For  16  apples,  how  many  oranges  can  be 
had,  by  giving  2  apples  for  1  orange  ? 

12.  How  many  primers,  at  2  cents  each,  can 
be  had  for  26  cents  ? 

13.  How  many  barrels  of  flour,  at  2  dollars 
a  barrel,  can  be  bought  for  24  dollars  ? 

14.  For  22  dollars,  how  many  sheep  may  be 
bought,  at  2  dollars  each  ? 

15.  How  many  melons,  at  3  dimes  each,  may 
be  had  for  18  dimes  ? 

16.  At  3  conN  caoh,  how  mrmy  tops  may  be 
had  for  6  cents  ? 

17.  If  1  peck  of  beans  coBt  3  dimes,  how 
many  pecks  can  be  bought  for  21  dimes  \ 


DIVISION. 


43 


LESSON    III. 


1. 

8 

are 

how 

many 

times 

4? 

2. 

12 

are 

how 

many 

times 

4? 

3. 

16 

are 

how 

many 

times 

4? 

4. 

5 

are 

how 

many 

times 

5? 

5. 

10 

are 

how 

many 

times 

5? 

6. 

20 

are 

how 

many 

times 

4? 

7. 

15 

are 

how 

many 

times 

5? 

8. 

28 

are 

how 

many 

times 

4? 

9. 

20 

are 

how 

many 

times 

5? 

10. 

32 

are 

how 

many 

times 

4? 

11. 

36 

are 

how 

many 

times 

2? 

12. 

28 

are 

how 

many 

times 

2? 

13. 

30 

are 

how 

many 

times 

5? 

14. 

25 

are 

how 

many 

times 

5? 

15. 

35 

are 

how 

many 

times 

5? 

16. 

36 

are 

how 

many 

times 

4? 

17. 

27 

are 

how 

many 

times 

3? 

18. 

36 

are 

how 

many 

times 

3? 

19. 

48 

are 

how 

many 

times 

4? 

20. 

48 

are 

« 

how 

many 

times 

3? 

LESSON    IV, 

1.  If  4  books  cost  8  cents,  what  will  1  book 

cost? 

ANALYSIS. — If  4  books  cost  8  cents,  1  book  wi  11  cost 
one-fourth  of  .8  cents,  which  is  2  cents. 

2.  If  4  oranges  cost  12  cents,  what  will  I 
orange  cost  ? 


4:4:  DIVISION. 

3.  If  4  lemons  cost  16  cents,  what  will  1 
lemon  cost  ? 

4.  If  a  boy  walk  20  miles  in  4  days,  how  far 
does  he  walk  in  1  day  ? 

5.  If  a  boy  divide  10  apples  equally  among  5 
of  his  playmates,  how  many  will  each  receive  ? 

6.  A   boy    distributed    15   walnuts  equally 
among  5   of  his   playmates ;    how  many  did 
each  receive  ? 

7.  A  man  gave  28  dollars  for  4  hogs;  how 
much  did  they  cost  each  ? 

8.  A  boy  sold   5  baskets  of  berries  for  20 
cents  ;  how  much  did  he  get  for  one  basket  ? 

9.  Mary  gave  35  c^nts  for  5  pencils ;   how 
much  were  they  each  ? 

10.  Margaret  gave  36  cents  for  4  spools  of 
thread  ;  how  much  did  she  pay  for  each? 

11.  Thornton  walked  27  miles  in  3  days; 
how  far  did  he  walk  each  day  ? 

12.  If  3  inkstands  cost  36  cents,  what  will 
1  inkstand  cost  ? 

13.  If  2  yards  of  calico  cost  36  cents,  how 
much  will  one  yard  cost  ? 

14.  If  4  pounds  of  beef  cost  32  cents,  what 
will  1  pound  cost  ? 

15.  If  2  balls  of  cotton  cost  28  cents,  what 
will  1  ball  cost  ? 

16.  If  3  melons  cost  30  cents,  what  will  1 
melon  cost  ? 

17.  A  man  sold  3  cows  for  48  dollars ;  how 
much  was  that  for  each  ? 

18.  Albert  gave  36  marbles  for  4  oranges ; 
how  many  marbles  did  he  give  for  1  orange  ? 


MULTIPLICATION   AITD   DIVISION.  ** 

LESSON    V. 

Multiplication  and  Division  Combined. 

1.  3  times  4  are  how  many  times  2  ? 

ANALYSIS. — 3  times  4  are  12.     12  is  as  many  times  $ 
as  2  is  contained  times  in  12,  which  are  6  times. 

2.  3  times     6  are  how  many  times  2  ? 

3.  3  times     8  are  how  many  times  2  ? 

4.  3  times  10  are  how  many  times  2  ? 

5.  3  times  12  are  how  many  times  2  ? 

6.  3  times  12  are  how  many  times  4  ? 

7.  4  times     4  are  how  many  times  2  ? 

8.  4  times     5  are  how  many  times  2  ? 

9.  4  times     6  are  how  many  times  3  ? 
j.0.  4  times     7  are  how  many  times  2  ? 

11.  4  times     8  are  how  many  times  2  ? 

12.  4  times     9  are  how1  many  times  6  ? 

13.  4  times  10  are  how  many  times  5  ? 

14.  4  times  11  are  how  many  times  2  ? 

15.  4  times  12  are  how  many  times  6  ? 

16.  4  times  12  are  how  many  times  3  ? 

17.  5  times     6  are  how  many  times  3  ? 

18.  5  times     8  are  how  many  times  4  ? 

19.  5  times    9  are  how  many  times  3  ? 

20.  5  times  10  are  how  many  times  2  ? 

21.  How  many  times  4  are  5  times  12  ? 

22.  How  many  times  3  are  6  times     4  ? 

23.  How  many  times  3  are  6  times     7  ? 

24.  How  many  times  3  are  6  times     5  ? 

25.  How  many  times  4  are  6  times     8  ? 

26.  How  many  times  3  are  6  times  10  ? 


7. 

8. 

9. 

10. 


MULTIPLICATION   AND  DIVISION. 


27. 

How 

many 

times 

3 

are 

6 

times 

11 

28. 

How 

many 

times 

10 

are 

8 

times 

5 

29. 

How 

many 

times 

4 

are 

8 

times 

7 

30. 

How 

many 

times 

6 

are 

8 

times 

9 

31. 

How 

many 

times 

5 

are 

8 

times 

10 

32. 

How 

many 

times 

3 

are 

9 

times 

6 

33. 

How 

many 

times 

6 

are 

9 

times 

8 

34. 

How 

many 

times 

15 

are 

9 

times 

10 

35. 

How 

many 

times 

6 

are 

9 

times 

12 

36. 

How 

many 

times 

7 

are 

2 

times 

14 

37. 

How 

many 

times 

5 

are 

10 

times 

7 

38. 

How 

many 

times 

7 

are 

3 

times 

14 

39. 

How 

many 

times 

9 

are 

12 

times 

6 

40. 

How 

many 

times 

4 

are 

12 

times 

9 

LESSON    VI. 

Practical  Questions,  combining  Multiplication  and  Division. 

1.  If  ^2  pears  cost  4  cents,  what  will  3  pears 
cost? 

ANALYSIS. — If  2  pears  cost  4  cents,  1  pear  will  cost 
one-half  of  4  cents,  which  is  2  cents.  If  1  pear  cost  2 
cents,  3  pears  will  cost  3  times  2  cents,  which  are  6 
cents. 

2.  If  2  pens  cost  6  cents,  what  will  5  pens  cost  ? 

3.  If  2  melons  cost  24  cents,  what  will  3 
melons  cost  ? 

4.  If  2  lemons  cost  8   cents,  what   will  4 
lemons  cost  ? 

5.  If  2  books  cost  10  dimes,  what  will  6 
books  cost  ? 


MULTIPLICATION   AND   DIVISION.  47 

6.  If  2  oranges  cost  6  cents,  what  will  10 
oranges  cost? 

7.  It  3  pine-apples  cost  36  cents,  what  will 
7  -pine-apples  cost  ? 

8.  If  3  slates  cost  30  cents,  what  will  5  cost  ? 

9.  If  3  pencils  cost  18  cents,  what  will  6 
pencils  cost  ? 

10.  If  3  pens  cost  9  cents,  what  will  8  cost  ? 

11.  If  3  caps  cost  12  dimes,  what  will  10 
caps  cost  ? 

12.  If  3  pairs  of  shoes  cost  6  dollars,  what 
will  8  pairs  cost  ? 

13.  If  3  men  can  earn  18  -dollars  a  week, 
how  many  dollars  can  8  men  earn  in  a  week  ? 

14.  If  3  candies  cost  6  cents,  what  will  12 
candies  cost  ? 

15.  If  4  calves  cost  16  dollars,  what  will  9 
calves  cost  ? 

16.  If  4  sheep  cost  12  dollars,  what  will  12 
sheep  cost  ? 

17.  If  four  men  cut  8  cords  of  wood,  how 
many  cords  will  9  men  cut  ? 

18.  If  7  quarts  of  milk  cost  35  cents,  what 
will  8  quarts  cost  ? 

19.  How  many  coats  can  be  cut  out  of  36 
yards  of  cloth,  if  4  coats  can  be  cut  out  of  12 
yards  of  the  same  kind  of  cloth  ? 

20.  What  will  30  pounds  of  sugar  cost,  if  6 
pounds  cost  30  cents  ? 

21.  "What  will  18  pounds  of  veal  cost,  if  6 
pounds  cost  42  cents  ? 

22.  What  will  13  pounds  of  pork  cost,  if  6 
pounds  cost  48  cents  J 


48  MULTIPLICATION   AND   DIVISION. 

23.  What  will  20  weeks'  board  come. to,  if  6 
weeks'  board  comes  to  12  dollars  ? 

21.  What  will  be  the  cost  of  25  bushels  of 
apples,  if  9  bushels  cost  90  cents  ? 

25.  What  will  14  pounds  of  cheese  cost,  if  8 
pounds  cost  40  cents  ? 

26.  If  6  men  can  do  a  certain  piece  of  work 
in  18  days,  in  how  many  days  can  12  men  do 
the  same  work  ? 

27.  Gave  for  a  quantity  of  cotton  72  dollars, 
and  sold  it  for  12  yards  of  cloth;  how  much 
did  the  cloth  cost  a  yard  ? 

28.  What  cost  10  cows,  if  3  cows  cost  45 
dollars  ? 

29.  If  4  oranges  are  worth  16  apples,  how 
many  apples  are  12  oranges  worth  ? 

30.  How  many  men  can,  in  4  days,  do  as 
much  work  as  8  men  can  in  7  days  ? 

31.  How  many  men  can,  in  3  days,  do  as 
much  work  as  9  men  in  5  days  ? 

32.  How  many  days  will  it  take  5  men  to  do 
what  it  takes  6  men  10  days  to  perform  ? 

33.  What  will  12  pounds  of  fish  cost,  if  8 
pounds  cost  72  cents  ? 

34.  What  will  15  yards  of  cloth  cost,  if  7 
yards  cost  35  dollars  ? 

35.  What  cost  14  geese,  if  9  cost  72  dimes  ? 

36.  What  cost  13  locks,  if  7 cost  70  cents? 

37.  What  cost  16  ducks,  if  5  cost  100  cents  ? 

38.  How  far  can  a  boy  travel  in  9  days,  if  in 
7  days  he  travel  63  miles  ? 

39.  How  far  could  a  man  ride  for  120  cents, 
if  for  40  cents  he  could  ride  8  miles  2 


COMPOUND     DENOMINATE 
NUMBERS. 


LESSON     I. 

TABLE  OF  UNITED  STATES  CURRENCY. 

10  Mills           make  1  Cent,  marked  ct. 

10  Cents              "      1  Dime,  "         di. 

10  Dimes,  or)      tf      *  Dollar  «         $ 
100  Cents        C                   °Uar' 

10  Dollars            "      \  Eagle,  K 

NOTE. — The  Canadian  currency  is  the  same  as  that  of  the  United 
States,  and  has,  in  addition,  a  Shilling,  which  equals  20  cents,  and  5 
shillings  make  1  dollar. 

1.  How  many  mills  in  6  cents  ? 

ANALYSIS  IST. — In  1  cents  there  are  10  mills,  therefore 
10  times  the  number  of  cents  equal  the  number  of  mills. 
10  times  6  are  60  mills. 

ANALYSIS  2o. — In  1  cent  there  are  10  mills,  and  in  6 
cents  there  are  6  times  10,  which  are  60  mills. 

2.  How  many  mills  in  1  cent  ?  in  2  cents?  in 
3  cents  ?  in  4  cents  ?  in  5  cents  ? 

3.  How  many  cents  in  1  dime  ?  in  3  dimes  ? 
in  4  dimes?   in  2  dimes?   in  5  dimes?   in  6 
dimes? 

4.  How  many  dimes  in  1  dollar  ?  in  2  dol- 
lars? in-  4  dollars?  in  3  dollars?  in  7  dollars? 
in  8  dollars  ?  in  9  dollars  ?  in  6  dollars  ? 

5.  How  many  dollars  in  1  eagle  ?  in  4:  eagles  ? 
in  3  eagles  ?  in  5  eagles  ?  in  9  eagles  ? 

5 


50  COMPOUND   NUMBERS. 

6.  In  50  mills  how  many  cents? 

ANALYSIS. — There  are  10  mills  in  1  cent,  therefore, 
one-tenth  of  the  number  of  mills  equals  the  number  of 

cents.  One-tenth  of  50  is  5  cents. 

7.  In  20  mills  how  many  cents  ? 

8.  In  30  cents  how  many  dimes  ? 

9.  In  60  cents  how  many  dimes  ? 

10.  In  70  cents  how  many  dimes  ? 

11.  In  80  cents  how  many  dimes  ? 

12.  In  90  cents  how  many  dimes  ? 

13.  In  20  dimes  how  many  dollars  ? 

14.  In  30  dimes  how  many  dollars  ? 

15.  In  90  dimes  how  many  dollars  ? 

16.  In  80  dimes  how  many  dollars  ? 

17.  In  40  dollars  how  many  eagles  ? 

18.  In  60  dollars  how  many  eagles  ? 


LESSON    II. 

TABLE  OF  ENGLISH 


4  Farthings  (qr.)  make  1  Penny,    marked  d. 
12  Pence  "       1  Shilling,        "        s. 

20  Shillings  "      1  Pound.          "        £. 

1.  How  many  pence  in  5  shillings  ? 

ANALYSIS.—  In  1  shilling  there  are  12  pence,  therefore 
12  times  the  number  of  shillings  equal  the  number  of 
pence.  12  times  5  are  60  pence. 

2.  How  many  farthings  in  2  pence?   in  4 
pence?  in  7  pence?  in  5  pence?  in  9  pence? 

3.  How   many  pence   in  4  shillings  ?   in  3 
shillings  ?  in  7  shillings  ?  in  8  shillings  ? 


COMPOUND  NUMBERS.  51 

X 

4.  How  many  shillings  in  2  pounds  ?  in  4 
pounds?   in  3   pounds?    in   7  pounds?    in   8 
pounds  ? 

5.  How  many   farthings   in   2  shillings,  2 
pence  and  2  farthings  ? 

6.  How  many  pence  in  1  pound  6  shillings! 

7.  How  many  farthings  in  1  pound  2  shil- 
lings and  3  pence  ? 


LESSON    III. 

TABLE  OF  TROY  WEIGHT. 

24  Grains  (gr.)    make  1  Pennyweight,  marked  pwt. 
20  Pennyweights   "      1  Ounce,  "        oz. 

12  Ounces  "      1  Pound,  "        ft. 

1.  How  many  grains  in  2  grains. 

ANALYSIS. — There  are  24  grains  in  1  pennyweight, 
therefore,  24  times  the  number  of  pennyweights  equal 
the  number  of  grains.  24  times  2  are  48  pennyweights. 

2.  How  many  pennyweights  in  2  ounces  ?  in 
3  ounces  ?  in  6  ounces  ? 

3.  How  many  ounces  in   2  pounds  ?   in  4 
pounds  ?  in  5  pounds  ? 

4.  How  many  pounds  in  60  ounces  ? 

ANALYSIS. — There  are  12  ounces  in  1  pound,  therefore 
one-twelfth  of  the  number  of  ounces  equals  the  number 
of  pounds.  One-twelfth  of  60  is  5  pounds. 

5.  How  many  ounces  in  80  pennyweights  ? 

6.  How  many  pounds  in  84  ounces  ? 


52  COMPOUND   NTTMBEES. 

LESSON    IV. 

TABLE  OF  APOTHECARIES'  WEIGHT. 

20  Grains  (gr.)  make  1  Scruple,  marked  B 

3  Scruples  "  1  Dram,  "  3 

8  Drams  "  1  Ounce,  § 

12  Ounces  "      1  Pound         "  lb 

1.  In  3  scruples  how  many  grains  ? 

2.  In  4  drams  how  many  scruples  ? 

3.  In  3  pounds  how  many  scruples  ? 

4.  In   5   drams  and  2  scruples  how  many 
grams  ? 

5.  In  1  pound  3  scruples,  how  many  grains  ? 

6.  In  2  drains  3  scruples  and  4  grains,  how 
many  grains  ? 

7.  In  48  drams,  how  many  ounces  ? 

8.  In  96  drams,  how  many  pounds? 


LESSON    Y, 

TABLE  OF  AVOIRDUPOIS  WEIGHT. 

16  Drams  (dr.)  make  1  Ounce,             marked  oz. 

16  Ounces  "      1  Pound,                   "        ft. 

25  Pounds  1  Quarter,                           gr. 

4  Quarters  "      1  Hundred-weight,  "        cwt. 

20  Hundred-weight  "      1  Ton,                        "        T. 

1.  How  many  drams    in    1   ounce?    in   2 
ounces  ?  in  5  ounces  ?  in  4  ounces  ? 

2.  How  many  ounces  in   2  pounds?   in  3 
pounds  ?  in  4  pounds  ?  in  5  pounds  ? 

3.  How  many  pounds  in  2  quarters?  in  8 
quarters  ?  in  4  quarters  ?  in  8  quarters  ? 


COMPOUND   NUMBERS.  53 

4.  How  many  quarters  in  2  hundred- weight  ? 

5.  How  many  hundred-weight  in  4  tons  ?  in 
3  tons?  in  5  tons? 

6.  How  many  ounces  in  32  drams  ? 

7.  How  many  pounds  in  48  ounces  ? 

8.  How  many  quarters  in  75  pounds  ? 

9.  How  many  hundred-weight  in  12  quar- 
ters? 

10.  How  many  tons  in  60  hundred-weight  ? 


LESSON    VI. 

TABLE  OF  CLOTH  MEASURE. 

2i  Inches  (in.)  make  1  Nail,  marked  na. 

4    Nails  "      1  Quarter  of  a  yard,     "        qr. 

4    Quarters          "      1  Yard,  "        yd. 

NOTE.— The  Flemish,  English,  and  French  ells  are  no  longer  used. 

1.  In  1  yard  how  many  quarters  ? 

2.  In   3   yards  and   3  quarters  how  many 
quarters  ? 

3.  In  3  quarters  how  many  nails  ? 

4.  In  2  qr.  and  3  na.  how  many  nails  ? 

5.  In  2  yards  how  many  nails  ? 

6.  In  3  yards  how  many  quarters  ? 

7.  In  32  nails  how  many  yards  ? 

8.  In  64:  nails  how  many  yards  ? 

9.  In   3   yards   and   3  quarters  how  many 
quarters  ? 

10.  In  4  yards  and  2  quarters  how  many 
quarters  ? 

11.  In  4:  yards  and  3  quarters  how  many 
quarters  ? 


COMPOUND  NUMBERS. 


LESSON    VII. 

TABLE  OF  LONG  MEASUBE. 


3    Barley-corns  (be.)  make  1  Inch,        marked  in. 

12    Inches 

1  Foot, 

ft- 

3    Feet 

1  Yard, 

yd. 

5i  Yards,  or  16£  Feet 

1  Rod 

rd. 

40    Rods,  or  220  yards 

1  Furlong, 

fur. 

8    Furlongs 

1  Mile, 

mi. 

3    Miles. 

1  League. 

le. 

60    Geographic,  or)       „      1  D                   «        dffj        0 
69^  Statute  Miles    f                  Degree,                  tfctf.  01 

360    Degrees                      the  Circumference  of  the  earth. 

4. 
5. 


1.  In  2  yards  how  many  inches  ? 

2.  In  4  rods  how  many  yards  ? 

3.  In  3  feet  how  many  barley-corns  ? 
In  2  furlongs  how  many  yards  ? 
In  4  miles  how  many  rods  ? 

6.  In  198  inches  how  many  yards? 

7.  In  320  rods  how  many  miles  ? 

8.  In  48  furlongs  how  many  leagues  ! 

9.  In  5280  feet  now  many  miles  ? 
10.  In  1  mile  how  many  feet  ? 


LESSON      VIII. 

TABLE  OP  LAND  on  SQUARE  MEASURE. 
144    Square  in.  (sq.  in.)  make  1  Square  ft.,  marked  sq.  ft. 


9     Square  feet 
30i  Sq.  yd.,  or  272J  ft. 
40     Sq.  rod,  or  poles 

4    Roods 
640    Acres 


1  Square  yd., 

1  Square  rod, 

1  Rood, 

1  Acre, 

1  Square  mile, 


sq.  yd. 
sq.  rd. 
R. 
A. 


1.  In  2  square  feet  how  many  square  inches  ? 


COMPOUND   NUMBERS. 


55 


2.  In  2  feet  square  how  many  square  inches  ? 

3.  In  27  sq.  ft.  how  many  square  yards  \ 

4.  In  1  square  rod  how  many  square  feet  ? 

5.  In  1  acre  how  many  rods  ? 

6.  In  4  acres  how  many  rods  ? 


LESSON    IX, 

TABLE  OF  SOLID  OK  CUBIC  MEASURE. 


1728  Cubic  in.  (cu.  £tt.)make  1  Cubic  foot,  marked  cu.ft. 
27  Cubic  feet 
40  ft  round  tim.,  or 
50  ft.  hewn  timber 
16  Cubic  feet 
8  Cord  feet,  or 
128  Cubic  feet 


Cubic  yard, 
1  Ton, 
1  Cord  foot, 
1  Cord  of  wood, " 


cu.  yd. 
T. 

c.ft. 
cd. 


A  pile  of  wood  8  feet  long,  4  feet  wide,  and  4  feet  high  is 
a  cord. 

1.  In  2  cords  how  many  cord  feet  ? 

2.  In  2  cords  how  many  cubic  feet  ? 

3.  In  3  cubic  yards  how  many  cubic  feet  ? 

4.  In  256  cubic  feet  how  many  cords  ? 

5.  In  54:  cubic  feet  how  many  cubic  yards  ? 


LESSON    X. 

TABLE  OF  WINE.  MEASURE. 


4    Gills  (gi.)                        mi 
2    Pints 
4    Quarts 
8H  Gallons 
42    Gallons 
63    Gallons,  or  2  barrels 
2    Hogsheads  (126  gals.) 
2    Pipes,  4  hhds.,  or  252  gals., 

ike  1  Pint,     mar 
1  Quart, 
1  Gallon 
1  Barrel 
I  Tierce, 
1  Hogshead, 
1  Pipe,            ' 
1  Tun, 

ked  pt. 

'     qt. 

<      gal. 
'      1)1)1. 
'      ti. 
1      hhd. 

:  * 

56  COMPOUND   NUMBERS. 

1.  How  many  gills  in  4  pt.  ?   in  5  pt.  ?  in 
3pt.? 

2.  How  many  pints  in  3  qt.  ?  in  2  qt.  ?   in 
5  qt.? 

3.  How  many  quarts  in  2  gal.  3   in  4  gal.  ? 
in  5  gal.  ? 

4.  How  many  gallons  in  2  tier.  ?  in  3  tier. 

5.  How  many  gallons  in  2  hhd.  ?  in  3  hhd.  ? 

6.  How  many  hogsheads  in  2  pipes  ?  in  4 
pipes  ? 

7.  How  many  gills  in  1  qt.  ?  in  3  qt.  ?  in 
5  qt.? 

8.  How  many  pints  in  3  gaL?   in  4  gal.? 

9.  How  many  pints  in  1  pipe  ? 

10.  How  many  qt.  in  32  gills  ?  in  64  gills  ? 

11.  How  many  gallons  in  32  pt.  ?  in  16  pt.  ? 

12.  How  many  gallons  in  64  gills  ? 

13.  How  many  hogsheads  in  504  qt.  ? 


LESSON    XI, 

TABLE  OF  DRY  MEASURE. 

2  Pints  (pt.)  make  1  Quart,        marked  qt. 

8  Quarts     »       "  1  Peck,  "       pk. 

4  Pecks  "  1  Bushel,  "        bu. 

8  Bushels  "  1  Quarter,          "        qr. 

36  Bushels  "  1  Chaldron,        "        ch. 

1.  In  2  quarts  how  many  pints? 

2.  How  many  pints  in  3  qt.  ?  in  4  qt.  ? 

3.  How  many  pints  in  1  peck  ?  in  2  pk. 

4.  How  many  qt.  in  3  pk.  ?  in  5  pk.  ? 

5.  How  many  qt.  in  2  bu.  ?  in  3  bu.  ? 

6.  How  many  bu.  in  8  pk.  ?  in  20  pk.  ? 


COMPOUND   NUMBE&S.  5 

7.  How  many  pecks  in  16  qt.  ?  in  24  qt.  ? 

8.  How  many  qt.  in  12  pt.  ?  in  18  pt.  ? 

9.  How  many  pecks  in  64  pt.  ?  32  pt.  ? 

10.  How  many  bu.  in  32  qt.  ?  in  64  qt.  ? 

11.  How  many  pecks  in  1  chaldron  ? 

12.  How  many  quarts  in  1  chaldron  ? 


LESSON    XII. 

TABLE  OF  TIME. 


60  Seconds  (sec.)     make  1  Minute,  marked  mi. 
60  Minutes 
24  Hours 

7  Days 

4  Weeks 

12  Calendar  months 
52  Weeks 


1  Hour, 
1  Day, 
1  Week 
1  Month, 
Year, 


1  Year, 


hr. 

da. 
wk. 
mo. 

yr. 

yr. 


The  following  table  exhibits  the  names  of  the 
months,  and  the  number  of  days  in  each. 


NAMES. 

1st    month,  January, 
2nd       "        February, 


•z  (  3d 
ll  4th 
&  (  5th 

£  (  6th 

I  \  7th 
I  (  8th 

§  (  9th 

I  -hoth 

5  (llth 
I  ]  12th 


March, 

April, 

May, 

June, 
July, 

August, 

September, 

October, 

November, 


DAYS.  * 

31. 

28,  in  leap  year  29. 

31. 
30.  * 
31. 

30. 
31. 
31. 

30. 
31. 
30. 


December,        3L 


58  COMPOUND    NUMBERS. 

The  following  lines  may  aid  in  remembering 
the  number  of  days  in  each  month  : 

"  Thirty  days  hath  September, 
April,  June,  and  November ; 
All  the  rest  have  thirty-one, 
Excepting  February,  all  alone, 
"Which  hath  twenty-eight  in  fine, 
Except  in  Leap-year,  twenty-nine." 

1.  Name  the  Winter  months,  and  the  mim> 
ber  of  days  in  each  month. 

2.  Name  the  Spring  months,  and  the  num- 
ber of  days  in  each  month. 

3.  Name    the   Summer   months,    and  the 
number  of  days  in  each  month. 

4.  Name    the   Autumn  months,   and  the  i 
number  of  days  in  each  month. 

5.  How  many  seconds  in  2  minutes  ?  in  4 
minutes  ?  in  3  minutes  ? 

6.  How  many  minutes  in  2  hours?   in  3  • 
hours  ?  in  4  hours  ? 

7.  How  many  hours  in  2  days  ?  in  5  days  ? 
in  3  days  ?  in  4  days  ? 

8.  How  many  days  in  3  weeks  ?  in  4  weeks  ? 
in  6  weeks  ?  in  2  weeks  ? 

9.  How  many  weeks  in  4  months?   in  6 
months?    in  3   months?   in   2  months?  in  5 
months  ? 

10.  How  many  weeks  in  2  years  ? 

11.  How  many  months  in  6  years? 


COMPOUND   NUMBEBS.  59 

12.  How  many  minutes  in  180  seconds?  in 
240  seconds  ? 

13.  How  many  hours  in  120  minutes  ?  in  360 
minutes  ? 

14:.  How  many   days   in  48  hours?    in  96 
hours  ?  in  72  hours  ? 

15.  How  many  weeks  in  21  days  ?  in  28  days  ? 
in  49  days  ? 

16.  How  many  months  in  12  weeks  ?  in  24 
weeks?  in  36  weeks? 

17.  How  many  hours  in  3600  seconds? 

18.  How  many  weeks  in  168  hours? 

19.  How  many  months  in  52  weeks  ? 

20.  How  many  days  in  3  weeks  and  3  days  ? 

21.  How  many  hours  in 4  days  and  4  hours? 


LESSON    XIII. 

TABLE  OF  CIRCULAR  MOTION. 

60  Seconds  (")  make  1  Minute,  marked  ' . 

60  Minutes  "      1  Degree,        "        ° 

30  Degrees  "      1  Sign,  "        sign. 

12  Signs,  or  360  Degrees     "      1  Circle,          "        0. 

1.  How  many  degrees  in  2  circles  ? 

2.  How  many  minutes  in  1  sign  ? 

3.  How  many  seconds  in  1  degree  ? 

4.  How  many  degrees  in  8  signs  ? 

5.  If  there  are  60  miles  in  1  degree,  how 
I  many  miles  in  4  degrees  ? 

6.  How  many  degrees  in  12  signs  v 


60  COMPOUND   ITUMBERS. 

LESSON    XIV, 

MISCELLANEOUS   TABLES. 
AVOIRDUPOIS  WEIGHT. 

A  gallon  of  train-oil  weighs  7t  Ib. 

A  stone  of  wire  10J- 

A  stone  of  iron,  or  horseman's  weight,  is  14 

A  peck  of  salt  weighs  14 

A  bushel  of  salt  56 

A  firkin  of  butter  "  56 


A  quintal  of  fish 

A  faggot  of  steel 

A  barrel  of  flour 

A  barrel  of  beef  or  pork 

A  barrel  of  potash 

A  fother  of  lead 


100 
120 
196 
200 
200 
19  cwt.  2  qrs. 


LONG  MEASURE. 
Inches     make  1  Hand.    Used  for  meas.  horses. 

(Used    by    sailors   for 
Feet         make  1  Fathom.  •<  meas.  ropes,  the  depth 

( of  water,  &c. 

Inches      make  1  Link  of  a  surveyor's  chain. 
100        Links,  or  6G  feet,  or  4  rods,  make  1  chain. 
80        Chains,  or  320  rods,  or)    .      „     -•      n 
1760  yards,  or  5280  feet ) 

SOLID  MEASURE. 

231      cubic  inches  make  1  Wine  gallon. 
282      cubic  inches  make  1  Beer  gallon. 
2150fi  cubic  inches  make  1  Bushel. 

LIQUID  MEASURE. 
10  Gallons  make  1  Anker. 
18  Gallons  make  1  Rundlet. 
42  Gallons  make  1  Tierce. 
84  Gallons  make  1  Puncheon. 
9  Gallons  make  1  Firkin  of  beer. 
18  Gallons  make  1  Kilderkin  of  beer. 
36  Gallons  make  1  Barrel  of  beer. 
54  Gallons  make  1  Hogshead  of  beer. 
108  Gallons  make  1  Butt. 


COMPOUND  OTMBEBS.  61 


TABLE. 

12  Single  things     make  1  Dozen,  -     marked  doz. 
12  Dozen  "      1  Gross,  "        gro. 

12  Gross  (144  doz.)     "      1  Great  Gross,   "        ff.ffro. 
20  Single  things         "      1  Score,  "        sco. 

5  Scores  "          100. 

TABLB  OF  PAPER. 

24  Sheets  of  paper  make  1  Quire. 
20  Quires  "       1  Ream. 

2  Reams  "       1  Bundle. 

10  Reams  "       1  Bale. 

TABLE  OF  PARCHMENT. 

12  Skins  make  1  Dozen. 

5  Dozen,  or  .60  Skins  "      1  Roll.   , 

TABLE  OF  BOOKS. 

When  a  sheet  of  paper  makes : 

2  leaves,  or    4  pages,  the  book  is  called  a,  folio  size. 

4  leaves,  or   .8  pages,  the  book  is  called  a  quarto         " 

8  leaves,  or  16  pages,  the  book  is  called  an  octavo        " 

12  leaves,  or  24  pages,  the  book  is  called  a  duodecimo  " 

18  leaves,  or  36  pages,  the  book  is  called  an  eighteenmo" 

ARITHMETICAL  SIGNS. 

1.  The  symbol  -f  is  called  plus,  and  is  the  sign  of 
addition.     Thus,  2  +   4  indicates  the  addition  of  2 
and  4. 

2.  The  symbol  —  is  called  minus,  and  is  the  sign  of 
subtraction.     Tims,  5  —  2  indicates  the  subtraction  of 
2  from  5. 

3.  The  symbol    x    is    the    sign  of   multiplication. 
Thus,  3x5  indicates  that  3  is  to  be  multiplied  by  5, 
or  5  by  3. 

4.  The  symbol  -f-  is   the  sign  of  division.      TLus, 
8-^2  indicates  the  division  of  8  by  2. 

5.  The  symbol  =  is  the  sign  of  equality.      Thus, 
4  +  6  =  10. 


62 


COMPOUND   NUMBERS 


ALIQUOT,  OR  EQUAL  PARTS  OF  A  DOLLAR. 


106 

cents 

— 

1 

dollar. 

75 

cents 

= 

I 

4 

(three-fourths) 

of 

a  dollar. 

50 

cents 

= 

\ 

(one-half) 

of 

a  dollar. 

33i 

cents 

= 

•£ 

(one-  third) 

of 

a  dollar. 

25 

cents 

= 

1 

4 

(one-fourth) 

of 

a  dollar. 

m 

cents 

= 

(one-eighth) 

of 

a  dollar. 

10 

cents 

= 

fa 

(one-tenth) 

of 

a  dollar. 

6i 

cents 

= 

As 

(one-sixteenth) 

of  a  dollar. 

5 

cents 

ss 

fa 

(one-twentieth) 

of 

a  dollar. 

4 

cents 

— 

2L5 

(one-twenty-fifth) 

of 

a  dollar. 

2 

cents 

•=. 

fa 

(one-fiftieth) 

of 

a  dollar. 

1 

cent 

—  I 

ID 

(one-hundredth) 

of 

a  dollar. 

NEW  YORK  CURRENCY. 


s.  d. 

0  6  are  6J-  cts. 

1  0    is  134  cts. 

1  6  are  18}  cts. 

2  0  are  25    cts. 

2  6  are  31  i  cts. 

3  0  are  37|  cts. 

3  G  are  43 }  cts. 

4  0  are  50    cts. 


s.  d. 

4  G  are  56  J:  cts. 

5  0  are  62^  cts. 

5  6  are  68 }  cts. 

6  0  are  75  cts. 
G  6  are  81  i  cts. 

7  0  are  87|  cts. 

7  6  are  93}  cts. 

8  0  are  100  eta 


ALIQUOT,  OR 

80  days  = 

15  days  = 

10  days  — 

6  days  = 

5  days  — 

3  days  = 

2  days  — 

1  day    = 


EQUAL  PARTS  OF 

1  month. 

i  (one-half)  of 
J  (  one-third)  of 
i  (one-fifth)  of 
£  (one-sixth)  of 
i1,}  (one-tenth)  of 
^  (one-fifteenth)  of 
g^"  (one-thirtieth)  of 


A  MONTH 

a  month. 
a  month. 
a  month. 
a  month. 
a  month. 
a  month. 
a  month. 


ALIQUOT,  OR  EQUAL  PARTS  OF  A  YEAR. 

12  months  =    1  year. 

6  months  —    £  (one-half)  of  a  year. 

4  months  —    •£  (one-third)  of  a  year. 

3  months  =    i  (one-fourth)  of  a  year. 

2  months  =    i  (one-sixth)  of  a  year. 

1  month    a=  iV  (one-twelfth)  of  a  year. 


FRACTIONS. 


LESSON    I, 

1.  Mary  has  4  apples,  and  Sarali  1  half  as 
many ;  how  many  has  she  ? 

AHAX.YSIS. — If  Maty  has  4  apples/and  Sarah  1  half  as 
many,  she  must  have  one-half  of  4  apples,  which  is  2 
apples. 

2.  Henry  is  8  years  old,  and  Harvey  is  1  half 
as  old  ;  how  old  is  Harvey  ? 

3.  Martin  has  6  marbles,  and  Matthew  1  half 
as  many ;  how  many  has  he  ? 

4.  If  you  divide  10  apples  equally  between  2 
boys,  what  part  of  them  will  each  receive  ? 

5.  What  is  1  half  of  10  ? 

6.  If  an  orange  cost  12  cents,  and  a  lemon 
1  half  as  much;    what  was  the   cost  of  the 
lemon  ? 

7.  If  3  apples  cost  6  cents,  what  part  of  6 
cents  will  1  apple  cost  ? 

8.  A¥hat  is  1  third  of  6  ? 

9.  What  is  1  half  of  4?  of  6  ?  of  8  ?  of  10 ? 
of  12?  of  14?  of  16?  of  18?  of  20?  of  24? 

10.  If  3  oranges  cost  9  cents,  what  part  of 
9  cents  will  1  orange  cost  ?  what  part  of  9  cents 
will  2  oranges  cost  ? 

11.  What  is  1  third  of  3  ?  of  6  ?  of  9  ?  of  12  ? 
of  15?  of  21?  of  24?  of  27?  of  302 

12.  If  1  quart  of  nuts  cost  12  cents,  what  will 
1  third  of  a  quart  cost  1 


64  FRACTIONS. 

13.  If  1  ton  of  hay  cost  $15,  what  will  1 
third  of  a  ton  cost  ? 

14.  If  1  bushel  of  apples  cost  21  cents,  what 
will  1  third  of  a  bushel  cost  ? 

15.  If  1  yard  of  shalloon  cost  24  cents,  what 
will  1  third  of  a  yard  cost  ? 

10.  If  1  quart  of  vinegar  cost  9  cents,  what 
will  1  third  of  a  quart  cost  ? 

17.  If  1  pound  of  candies  cost  12  cents,  what 
part  of  12  cents  will  1  third  of  a  pound  cost? 
what  part  of  12  cents  will  2  thirds  of  a  pound 
£ost  ? 

18.  What  is  1  third  of  12  ? 

19.  If  1  third  of  12  is  4,  what  is  2  thirds 
of  12? 

20.  "What  is  1  third  of  6  ?  2  thirds  of  6  ?   4 
thirds  of  G  ?  3  thirds  of  6  ?  5  thirds  of  6  ? 

21.  If  a  barrel  of  flour  cost  9  dollars,  what 
will  1  third  of  a  barrel  cost?  2  thirds? 

22.  What  is  1  fourth  of  12?  2  fourths  of  12? 

3  fourths  of  12? 

23.  If  a  barrel  of  fish  cost  $12,  what  will  1 
fourth  of  a  barrel  cost  ?   2  fourths  ?  3  fourths  ? 

4  fourths  ? 

24-.  What  is  1  fifth  of  15  ?  2   fifths  of  15  ?  3 
fifths  of  15  ?  4  fifths  of  15  ?  5  fifths  of  15  ? 

25.  If  a  ton  of  hay  cost  $15,  what  will  1  fifth 
of  a  ton  cost?   2  fifths?   3  fifths?   4  fifths?   5 
fifths  ? 

26.  What  is  2  thirds  of  24  ?   3  fourths?   3 
eighths  ?  2  fourths  ? 

27.  What  is  3  fifths  of  20  ?  7  eighths  of  64  ? 
4  sevenths  of  56  ? 


FRACTIONS.  65 

27.  "What  do  you  understand  by  1  fourth  ? 

3  fourths  ? 

ANSWER. — When  a  thing  is  divided  into  four  equal 
parts,  1  of  these  parts  is  called  1  fourth,  and  3  of  these 
parts  are  called  3  fourths. 

23.  What  do  you  understand  by  2  fifths  ?  3 
fifths  ?  4  fifths  ? 

29.  What  do  you  understand  by  3  sevenths  j 

4  sevenths  ?  5  sevenths  ?  6  sevenths  2 

30.  How  many  thirds  in  1  ? 

31.  How  many  fifths  in  1  ? 

32.  How  many  fourths  in  1  ? 

33.  How  many  tenths  in  1  ? 

34.  How  many  ninths  in  1  ? 

35.  How  many  twelfths  in  1  ? 

36.  What  is  1  seventh  of  $28  ?    2  sevenths 
of  $28?    3  sevenths?   4  sevenths?   6  sevenths? 

5  sevenths? 

37.  If  a  coat  cost  $20,  and  a  pair  of  panta- 
loons 1  fourth  as  much,  what  is  the  cost  of  the 
pantaloons  ? 

38.  If  a  pound  of  cheese  cost  9  cents?  what 
will  2  thirds  of  a  pound  cost  ? 

39.  If  12  oranges  cost  36  cents,  what  part 
of  36  cents  will  1  orange  cost?    2  oranges?   4 
oranges  ?  3  oranges  ?   5  oranges  ?  9  oranges  ?   8 
oranges  ? 

40.  What  is  1  twelfth  of  36  ?  2  twelfths  of 
36  ?    5  twelfths  of  36  ?    4  twelfths  of  36  ?    6 
twelfths  of  36?    9  twelfths?    8  twelfths?    10 
twelfths?  11  twelfths? 

41.  Rachel  has  14  primers,  and  Anthony  5 
seventh}  as  many ;  how  many  has  he ! 


66  FRACTIONS. 

42.  Abner  is  15  years  old,  and  Albert  is  4 
fifths  as  old ;  how  old  is  he  ? 

43.  Augustus  has  40  cents,  and  Augusta  has 
5  eighths  as  many  ;  how  many  has  she  ? 

44.  Martin  had  25  marbles,  and  gave  3  fifths 
of  them  to  Moses ;  how  many  had  he  remain- 
ing, and  how  many  did  he  give  to  Moses  ? 

45.  Morgan  had  21  fire-crackers,  and  Nathan 
had  8  sevenths  as  many  ;   how  many  had  he  ? 

46.  Matthew  had  45  apples,  and  Marvin  had 
5  ninths  as  many  ;  how  many  had  he  ? 

47.  Dubois  is  42  years  old,  and  his  father  is 
9  sixths  as  old ;  how  old  is  he  ? 

48.  A  farmer,  having  72  sheep,  lost  1  ninth 
of  them ;  how  many  had  he  remaining  ? 

49.  A  man  bought  ahorse  for  60  dollars,  and 
a  cow  for  3  fifths  as  much  ;  what  was  the  cost 
of  the  cow  ? 

50.  In   a   certain  school  there  are  9  girls, 
and  8  thirds  as  many  boys  ;  required  the  num- 
ber of  beys,  and  the  number  of  boys  and  girls 
together  ? 


LESSON    II. 

1.  3  fourths  of  12  are  how  many  times  3  ? 

ANALYSIS. — 1  fourth  of  12  is  3,  and  3  fourths  are  3 
times  3,  which  are  9.  9  is  as  many  times  8,  as  3  is 
contained  in  9,  which  are  3  times.  Therefore,  3  fourths 
of  12  are  3  times  3. 

2.  2  thirds  of  12^are  how  many  times  2  ? 

3.  2  thirds  of  15  arc  how  many  times  2  I 


FRACTIONS.  67 

4.  2  thirds  of  24  are  how  many  times  4  ? 

5.  2  fourths  of  12  are  how  many  times  6  ? 

6.  2  fourths  of  16  are  how  many  times  4  ? 

7.  3  fourths  of  16  ai?e  how  many  times  6  ? 

8.  2  thirds  of  21  are  how  many  times  7  ? 

9.  2  thirds  of  30  are  how  many  times  5  ? 

10.  2  thirds  of  27  are  how  many  times  6  ? 

11.  3  fourths  of  24  are  how  many  times  9  ? 

12.  3  fourths  of  36  are  how  many  times  9 .? 

13.  2  fourths  of  36  are  how  many  times  6  ? 

14.  3  fourths  of  28  are  how  many  times  7 1 

15.  3  fifths  of  20  are  how  many  times  6  ? 

16.  4  fifths  of  20  are  how  many  times  8  ? 

17.  4  fifths  of  15  are  how  many  times  6? 

18.  2  fifths  of  20  are  how  many  times  2? 

19.  3  sixths  of  24  are  how  many  times  6  ? 

20.  5  sixths  of  60  are  how  many  times  2  ? 

21.  2  sixths  of  72  are  how  many  times  6  ? 

22.  2  sevenths  of  42  are  how  many  times  3  ? 

23.  4  sevenths  of  42  are  how  many  times  6  ? 

24.  3  sevenths  of  70  are  how  many  times  5  ? 

25.  5  sevenths  of  28  are  how  many  times  2  ? 

26.  5  eighths  of  32  are  how  many  times  10  ? 

27.  6  eighths  of  48  are  how  many  times  12  ? 

28.  8  ninths  of  36  are  how  many  times  2  ? 

29.  9  tenths  of  40  are  how  many  times  6  ? 

30.  9  twelfths  of  96  are  how  many  times  6  ? 

31.  7  eighths  of  64  are  how  many  times  4  ? 

32.  7  sixths  of  54  are  how  many  times  3  ? 

33.  7  fourths  of  24  are  how  many  times  6  ? 

34.  8  tenths  of  30  are  how  many  times  4  ? 

35.  6  ninths  of  72  are  how  many  times  12! 


68  FKACTKXffS. 

LESSOR    III. 

1.  4  fifths  of  15  are  how  many  times  1  half 
of  12? 

2.  2  thirds  of  12  are  how  many  times  1  third 
of  6? 

3.  2  fourths  of  20  are  how  many  times  1  half 
of  20? 

4C  3  fourths  of  16  are  how  many  times  1  third 
of  18? 

5.  3  fifths  of  20  are  how  many  times  1  fourth 
of  24? 

6.  3  fifths  of  30  are  how  many  times  1  half 
of  18? 

7.  4  fifths  of  30  are  how  many  times  1  eighth 
of  64? 

8.  3  fourths  of  24  are  how  many  times  1  fifth 
of  45? 

9.  5  sixths  of  54  are  how  many  times  1  third 
of  9? 

10.  2  thirds  of  36  are  how  many  times  2 
thirds  of  9  ? 

11.  2  thirds  of  24  are  how  many  times  2 
thirds  of  6  ? 

12.  2  fifths  of  45  are  how  many  times  2  fifths 
of  15  ? 

13.  3  fifths  of  50  are  how  many  times  2  sixths 
of  18  ? 

14.  6  eighths  of  48  are  how  many  times  2 
fifths  of  15  ? 

15.  8  ninths  of  27  are  how  many  times  1 
ftmrtli  nf  2-1  ? 


FRACTIONS. 


16c  7  eighths  of  64  are  how  many  times  2 
sixths  of  42  1 

17.  3  ninths  of  108  are  how  many  times  3 
fourths  of  16  ? 

18  4  sevenths  of  84  are  how  many  times  4 
fifths  of  30  ? 


LESS  OK    IV, 

1.  If  2  thirds  of  an  orange  cost  4  cents,  what 
will  1  orange  cost  ? 

ANALYSIS. — If  2  thirds  of  an  orange  cost  4  cents,  1 
third  will  cost  1  half  of  4  cents,  which  is  2  cents.  If 
1  third  of  an  orange  co&t  2  cents,  3  thirds,  or  1  orange, 
will  cost  3  times  2  cents,  which  are  6  cents. 

2.  If  2  thirds  of  a  melon  cost  6  cents,  what 
will  1  third  of  a  melon  cost  ? 

3.  If  3  fourths  of  a  pound  of  sugar  cost  9 
cents,  what  will  1  fourth  ol  a  pound  cost  ? 

4.  If  2  thirds  of  a  pound  of  ginger  cost  8 
cents,  what  will  1  third  of  a  pound  cost  ? 

5.  If  4  thirds  of  a  pound  of  spice  cost  12 
cents,  what  will  1  third  of  a  pound  cost  ? 

6.  If  $8  will  buy  2  fifths  of  a  barrel  of  fish 
what  will  1  fifth  of  a  barrel  cost  ? 

7.  If  3  fourths  of  a  pound  of  cinnamon  cost 
9  cents,  what  will  1  fourth  of  a  pound  cost  ? 

8.  What  will  1  sixth  of  a  yard  of  cloth  cost, 
if  4  sixths  of  a  yard  cost  120  cents  ? 

9.  What  will  1  seventh  of  a  hogshead  of 
molasses  cost,  if  5  sevenths  of  a  hogshead  cost 
$15! 


70  FKACTIONS. 

10.  If  2  thirds  of  a  barrel  of  fish  cost  $8, 
what  will  one  barrel  cost  ? 

11.  If  3  fourths  of  a  bushel  of  wheat  cost  9 
dimes,  what  will  1  bushel  cost  ? 

12.  If  4  fifths  of  a  box  of  raisins  cost  12 
dimes,  what  will  one  box  cost  ? 

13.  If  6  eighths  of  a  yard  of  broadcloth  cost 
30  dimes,  what  will  1  yard  cost  ? 

14.  If  3  fourths  of  a  barrel  of  flour  cost  $6, 
what  will  1  barrel  cost  ? 

15.  If  2  fifths  of  a  barrel  of  fish  cost  $8, 
what  will  1  barrel  cost  ? 

16.  If  3  fourths  of  a  pound  of  cinnamon  cost 
12  cents,  what  will  1  pound  cost  ? 

17.  If  4  sixths  of  a  barrel  of  sugar  cost  $12, 
what  will  1  barrel  cost  ? 

18.  If  5  sevenths  of  a  box  of  boots  cost  $20, 
what  will  1  box  of  boots  cost  ? 

19.  It  4  ninths  of  a  hogshead  of  molasses  cost 
$20,  what  will  1  hogshead  cost  ? 

20.  If  2  fifths  of  the  cost  of  a  wagon  were 
[),  what  was  the  cost  of  the  wagon  2 


LESSON    V. 

1.  6     is     |     of    what     number? 

ANALYSIS. — If  2  thirds  of  some  number  is  67  1  third 
of  that  number  is  one-half  of  6,  which  is  3.  If  one-third 
of  that  number  is  3,  three-thirds,  which  is  that  number, 
is  3  times  3,  which  are  9,  Therefore,  6  is  two-thirds 
of  9. 

2.  8     is     |     of    what    number! 
8.      4    is     |    of    what    number  ? 


FRACTIONS,  71 

4.       10  is  |  of  what  number  ? 

12  is  |  of  what  number  ? 

12  is  |  of  what  number  ? 

7.  12  is  f  of  what  number  ? 

8.  9  is  |  .of  what  number  ? 

9.  12  is  f  of  what  number  ? 

10.  12  is  f  of  what  number? 

11.  15  is  |  of  what  number  ? 

12.  16  is  |  of  what  number  t 

13.  16  is  f  of  what  number  ? 

14.  18  is  |  of  what  number  ? 

15.  25  is  |  of  what  number? 

16.  26  is  |  of  what  number? 

17.  20  is  f  of  what  number  ? 

18.  30  is  |  of  what  number  ? 

19.  36  is  f  of  what  number.! 

20.  36  is  of  what  number  f 


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